It is popularly taught that the reformers declared five distinctive elements of theology that differentiated them from Rome: salvation by grace alone, through faith alone, in Christ alone, for the glory of God alone, as sufficiently taught in Scripture alone. They quoted the church fathers in support of their views to demonstrate that they weren't teaching novelties or heresies and they showed particular deference to Augustine. But did Augustine actually teach the doctrine described in the five solas?
Yes - the wikipedia article on sola fide baldly asserts that Augustine is among the "Church Fathers whom Protestant apologists believe taught the doctrine of Sola Fide (although Catholic and Orthodox apologists quote the same fathers as supporting a justification that includes works)."
Confusion in this regard, results from differing definitions of sola fide particularly between proponents and opponents. It should be correctly understood to mean: Justification comes only by grace through faith, not by any merit of works. It should not be construed so as to deny that: good works are (necessary) evidence of saving faith. Those who do so, are creating a straw man of the sola fide position, which is further clarified by:
The relationship of faith and good works is one that may be distinguished but never separated...if good works do not follow from our profession of faith, it is a clear indication that we do not possess justifying faith. The Reformed formula is, “We are justified by faith alone but not by a faith that is alone. - R.C. Sproul (as quoted in wikipedia)
Since Protestant apologists are in a better position to define what they mean by sola fide than their Catholic and Orthodox critics, and have adopted Augustine as a champion of the doctrine, their view is to be definitely preferred in this matter.
Another answer has (prior to a most judicious edit) profferred Augustine's On Grace and Free Will as proof positive that he does not teach sola fide, on reviewing the work however, I find it thoroughly consistent with a sola fide perspective. Consider chapters 16 & 17 of this work in their entirety, that the fair-minded may judge:
Chapter 16 [VII.]— Paul Fought, But God Gave the Victory: He Ran, But God Showed Mercy.
Let us, therefore, consider those very merits of the Apostle Paul which he said the Righteous Judge would recompense with the crown of righteousness; and let us see whether these merits of his were really his own— I mean, whether they were obtained by him of himself, or were the gifts of God. "I have fought," says he, "the good fight; I have finished my course; I have kept the faith." 2 Timothy 4:7 Now, in the first place, these good works were nothing, unless they had been preceded by good thoughts. Observe, therefore, what he says concerning these very thoughts. His words, when writing to the Corinthians, are: "Not that we are sufficient of ourselves to think anything as of ourselves; but our sufficiency is of God." 2 Corinthians 3:5 Then let us look at each several merit. "I have fought the good fight." Well, now, I want to know by what power he fought. Was it by a power which he possessed of himself, or by strength given to him from above? It is impossible to suppose that so great a teacher as the apostle was ignorant of the law of God, which proclaims the following in Deuteronomy: "Say not in your heart, My own strength and energy of hand has wrought for me this great power; but you shall remember the Lord your God, how it is He that gives you strength to acquire such power." Deuteronomy 8:17 And what avails "the good fight," unless followed by victory? And who gives the victory but He of whom the apostle says himself, "Thanks be to God, who gives us the victory through our Lord Jesus Christ"? 1 Corinthians 15:57 Then, in another passage, having quoted from the Psalm these words: "Because for Your sake we are killed all the day long; we are accounted as sheep for slaughter," he went on to declare: "Nay, in all these things we are more than conquerors, through Him that loved us." Romans 8:37 Not by ourselves, therefore, is the victory accomplished, but by Him who has loved us. In the second clause he says, "I have finished my course." Now, who is it that says this, but he who declares in another passage, "So then it is not of him that wills, nor of him that runs, but of God that shows mercy." Romans 9:16 And this sentence can by no means be transposed, so that it could be said: It is not of God, who shows mercy, but of the man who wills and runs. If any person be bold enough to express the matter thus, he shows himself most plainly to be at issue with the apostle.
Chapter 17.— The Faith that He Kept Was the Free Gift of God.
His last clause runs thus: "I have kept the faith." But he who says this is the same who declares in another passage, "I have obtained mercy that I might be faithful." 1 Corinthians 7:25 He does not say, "I obtained mercy because I was faithful," but "in order that I might be faithful," thus showing that even faith itself cannot be had without God's mercy, and that it is the gift of God. This he very expressly teaches us when he says, "For by grace are you saved through faith, and that not of yourselves; it is the gift of God." Ephesians 2:8 They might possibly say, "We received grace because we believed;" as if they would attribute the faith to themselves, and the grace to God. Therefore, the apostle having said, "You are saved through faith," added, And that not of yourselves, but it is the gift of God. And again, lest they should say they deserved so great a gift by their works, he immediately added, "Not of works, lest any man should boast." Ephesians 2:9 Not that he denied good works, or emptied them of their value, when he says that God renders to every man according to his works; Romans 2:6 but because works proceed from faith, and not faith from works. Therefore it is from Him that we have works of righteousness, from whom comes also faith itself, concerning which it is written, "The just shall live by faith." Habakkuk 2:4
It is certainly a major counter-argument that Luther himself believed Augustine's soteriology to be deficient (evidenced in the quotes by the afore-mentioned opposing answer), an (admittedly weak) riposte is that Luther was not the only reformer to examine Augustine's work and define sola fide - other Protestant apologists evidently disagree with Luther and think Augustine's divergences from Protestant soteriology to be trivial (cf. BB Warfield's quote that was the genesis of the preceding question to this: "the Reformation was a triumph of Augustine's soteriology over his ecclesiology" and the extent to which Calvin drew from Augustine as evidenced in this Q&A).
Well, at least this appears to be Martin Luther's answer
Augustine has sometimes erred and is not to be trusted. Although good and holy, he was yet lacking in the true faith, as well as the other fathers...But when the door was opended for me in Paul, so that I understood what justification by faith is, it was all over with Augustine. (Luther's Works 54, 49)
It was Augustine's view that the law...if the Holy Spirit assists, the works of the law do justify...I reply by saying "No". (Luther's Works 54, 10)
As to your statement about the popular belief that the reformers (and their descendants) frequently quoted a plethora of Church Fathers to demonstrate the legitimacy of their doctrine...
This is simply not true. Augustine is for the most part the only Church Father cited by Luther and Calvin. The early reformers relied virtually entirely upon Scripture to formulate doctrine.
The Protestant Confession of Augsburg (1530) in Article 20 cites Augustine as a supporter of the Protestant doctrine of Sola Fide: “Augustine, in many volumes, defends grace and the righteousness of faith, over against the merits of works."
It would appear, however, that even today there are different opinions. Augustine, to me at least, appears to have taught what looks like a combination of the two, if not that then certainly not Sola Fide itself.
The article below (though appearing to be a personal blog, and also sources the above quote from the Confession) notes different passages Augustine wrote regarding "faith alone" AND "faith through works". http://www.willcoxson.net/faith/augprot2.htm
St. Augustine taught one can lose their salvation by their actions (which protestants call 'works') even if they have the faith - this contradicts the five solas and Luther's concept of Simul Iustus et Peccator (at the same time just and a sinner)
St. Augustine on how mortal and venial sins are forgiven
“But do not commit those sins on account of which you would have to be separated from the Body of Christ; perish the thought! For those whom you see doing penance have committed crimes, either adultery or some other enormities: that is why they are doing penance. If their sins were light, daily prayer would suffice to blot them out. In the Church, therefore, there are three ways in which sins are forgiven: in Baptism, in prayer, and in the greater humility of penance; yet, God does not forgive sins except to the baptized.” (Augustine, Sermon to Catechumens, on the Creed, AD 395)
The definitive difference between what St. Augustine believed and what Luther in all honesty came up with himself is quite different. It's like this:
St. Augustine taught that grace is itself transformative and is infused into the soul of humanity, whereby changing their condition and makes the sinner righteous before God. So that when God sees the persons soul, he sees someone who is truly righteous. He teaches that we become a new creation and receive a share in God's very own nature. (2 Peter 1:4). This is what Catholics mean when we speak of sanctifying grace. It is the grace that is a share in God's very own nature. So now it is mankind's ability to love God and love neighbor, and that is what justifies us. Since we have been changed interiorly, we are now held accountable for our deeds by choosing with our own free will to cooperate with the God's Grace. So, it follows that we can turn back from God and choose not to live by the spirit it and live again by the flesh. (Galatians 5)
Augustine's favorite verse seems to be Romans 5:5 (random note) The reformers truly hinged their ideas on an incomplete understanding of what is taught in Romans 4. This is where they get their supposed doctrine of imputed righteousness.
It's important to note that St. Augustine had a very dim view of human freedom but still believed that mankind was still free in their fallen state. It is true that as Augustine ages you see development in his doctrine and he typically we seem more rigorous. It seems his view of original sin is close to Calvin's in some respects, and that his view of Predestination of the saints is also borderline. Personally, I don't believe he held to the Calvinist idea of double predestination, but it does come much closer. Later, Alexander of Hales would codify and sort of standardized the Augustinian orders teaching on Predestination.
So for Luther......
Luther believed that Justification by faith alone meant that the sinner is accounted righteous by the imputation of Christ's Righteousness. In other words the sinner is covered with the righteousness of Christ and Christ imputes the sin's of the world to himself so when God sees the sinner he sees the sinner clothed with the righteousness of Christ and when God sees Jesus he sees the sin's of the world and therefore punishes Christ. Whereby, God punishes the innocent, and acquits the guilty. You and I in theory get off scot-free. The sacrifice of Christ doesn't actually changes my at the time of Justification, Humanity still remains intrinsically sinful, but overtime I can actually grow in sanctification but it doesn't count towards my justification. So, over the course of my life I can be at enmity with the God if I'm one of the elect and still be justified.
The Big thing to remember is that in Luther's belief the sacrifice of the cross doesn't actually change me, it just forgives my sin and leaves me in my sinful state. The problem of sin was not solved on the cross.
St. Augustine taught as well as the Catholic Church to this day teaches that yes the problem of sin was solved on the cross and that Jesus out of an act of obedience sacrificed himself for our sins to repair what was lost as a result of the fall with Adam and Eve. We are now set free, and now are under grace and live by faith. It is love that justifies us, because the God is love, and therefore love indwells within us, so it is love that is fulfillment of the law. That is historical understanding of the doctrine taught for 1500 hundreds till Mr. Luther and his gang started coming up with their own doctrines. Luther didn't get his doctrine from St. Paul, St. Augustine, or any other church father, no no, his doctrine was made up whole cloth and was largely influenced by 14th century Occamist thought that was in the drinking water at the time. This school of thought influenced Martin Luther through the likes of Charles Biel and other fellas like these. My recommendation would be to read the definitive history of the doctrine which was written by a Protestant scholar by the way. It's titled Istitua Dei by Allister Mcgrath. If any of you are familiar with Historical theology, I'm sure you may have heard of it or read it even. In the book, Mcgrath will freely admit to you, that St. Augustine's doctrine of Grace, Justification, original sin, free will, salvation were wholly Catholic, and that the Reformers (Luther and Calvin) didn't get their doctrines from him or any other church father, no no, they got theirs from some where else.