If the Church of Jesus Christ of Latter-day Saints is neither Catholic nor Protestant then what authority is their Church based upon

Question

I realise there are some significant theological differences between LDS, Catholicism and Protestantism, mainly to do with the Trinity and the person of Jesus Christ. LDS doctrine recognizes Jehovah as the pre-mortal name of Jesus, who was created as a spirit son, before coming to earth as God the Son incarnate.

This official LDS article says that after the deaths of Jesus Christ and the Apostles apostasy became widespread and “lasted until Heavenly Father and His Beloved Son appeared to Joseph Smith in 1820 and initiated the restoration of the fulness of the gospel.”

I understand that the Church does not accept various creeds from the fourth and fifth centuries A.D. and that those creeds do not reflect the thinking or beliefs of “the New Testament church”. From this I can only conclude that they are neither Catholic nor Protestant.

What then is the foundation for this “New Testament church”? Is it based on the New Testament of the Holy Bible, or is it based on other sources? If it is based on other sources, please name them.

Edit: Please note I want the official LDS answer to this question, especially as to the basis of their "New Testament Church".

Answer 1

From Authority in the Church

Christian churches regard the question of authority — the divine right to preach, act in the name of God and direct the Lord’s church — in different ways. Some, like the Roman Catholic, Orthodox and Coptic churches, emphasize a continuous line of authority from the early apostles. Some who broke away from those churches say they find authority in the inerrancy of the Bible. Others rely heavily on a sense of “calling” to the ministry. Latter-day Saints have a distinctive view of priesthood authority that helps define them.

The New Testament describes the church established by Jesus Christ as one with structure and form. The apostles were at its head, and as recipients both of ordained authority and revelation, they were charged with guiding the church and keeping its doctrines pure as it expanded throughout the known world.

...

For Latter-day Saints, the restoration of priesthood authority in the first half of the 19th century was a literal act through angelic visitations from those who held the authority anciently. Divine authority was restored to The Church of Jesus Christ of Latter-day Saints through a visitation of the resurrected John the Baptist in 1829 near Harmony (now Oakland), Pennsylvania, and sometime afterwards through the appearance of the resurrected ancient apostles Peter, James and John.

Today, all members of The Church of Jesus Christ of Latter-day Saints who hold the priesthood trace their authority directly to these visitations and bestowal of the priesthood of God on Joseph Smith and early leaders of the Church. A person receiving the priesthood today customarily sits while a person who already holds the priesthood stands and places his hands on the recipient’s head and formally confers that authority.

See also:

• Gospel Topics: Restoration of the Priesthood
  • Study Guide
• Topical Guide: Church Organization (biblical references to New Testament church organization)

_{emphasis mine}

Answer 2

The following official article Frequently Asked Questions confirms that the Church of Jesus Christ of Latter Day Saints is neither Protestant nor Catholic and rejects the third and fourth centuries creeds:

The Church rejects the creeds that developed in the third and fourth centuries that are now embraced by many other Christian churches.

The Church of Jesus Christ of Latter-day Saints is a Christian church but is neither Catholic nor Protestant. Rather, it is a restoration of the Church of Jesus Christ as originally established by the Savior in the New Testament of the Bible.

According to Joseph Smith's written testimony of his First Vision:

I saw a pillar of light exactly over my head, above the brightness of the sun, which descended gradually until it fell upon me...When the light rested upon me I saw two Personages, whose brightness and glory defy all description, standing above me in the air. One of them spake unto me, calling me by name and said, pointing to the other—This is My Beloved Son. Hear Him!

My object in going to inquire of the Lord was to know which of all the sects was right, that I might know which to join. No sooner, therefore, did I get possession of myself, so as to be able to speak, than I asked the Personages who stood above me in the light, which of all the sects was right (for at this time it had never entered into my heart that all were wrong)—and which I should join.

I was answered that I must join none of them, for they were all wrong; and the Personage who addressed me said that all their creeds were an abomination in his sight; that those professors were all corrupt; (Joseph Smith History 1:16-19)

I submit this information to clarify the official view of the Church of Jesus Christ of Latter Day Saints.