I understand that for the Jews, the beginning of the Sabbath is at 5 PM on Friday. So why then does Sabbath start at sundown on Friday for the Seventh Day Adventists?
Seventh Day Adventism is what is known as a restorationist movement. This term is a references to their belief that something fundamental was corrupted or lost in Christianity and that their beliefs have unique insight to restore what was lost to the way it was supposed to me.
In the case of this question, they belief that the vast majority of Christianity from New Testament times on downward erred in their belief that the proper day to worship God changed after the resurrection. Throughout the Old Testament God's people always used the 7th day of the week (Saturday) as described in Genesis as the day set apart for the sabbath. Jews to this day continue that tradition.
Christians on the other hand believe that a change occurred when Christ was raised from the dead that in an senses sanctified that day, which happened to be the 1st day of the week (Sunday). Starting even in the pages of the New Testament you will find believers regularly meeting for worship, prayer, study of the Word, and sacraments on the 1st day of the week. Not a lot of explanation is given, everybody seems to just take it for granted that this was right and proper.
The SDA argument is that even these early Christians erred and that no direct mandate was given that would supersede the creation mandate for the 7th day (Saturday). They believe most of NT Christianity (and the 1900 some years since) was corrupted until their own prophet Ellen G. White set the record straight.
In the case of SDA, they have many beliefs that are different from mainstream Christianity besides just their meeting on the 7th day rather than the 1st. Similar 19th century revelations that "set the record straight" and (in their view) fix corrupted beliefs involve dietary restrictions (also from the Old Testament, discounting the revelations given to Peter about all foods being clean), and not believing in an eternal hell at all.
Seventh Day Adventists believe what the word of God teaches:
Genesis 1:5 God called the light “day,” and the darkness he called “night.” And there was evening, and there was morning—the first day.
We can see clearly that there was evening first followed by the morning i.e. a 24 hour day begins with the evening which God called "Night" which then is followed by the morning.
Thus according to God's reckoning the day begins with the evening (which begins with the sunset) and ends the next day evening. That is why Seventh Day Adventists keep the Sabbath thus.
Contrary to the popular belief, early Christians kept the Seventh Day Sabbath as the holy day. The Author of Hebrews says
For somewhere he has spoken about the seventh day in these words: “On the seventh day God rested from all his works.”[c] 5 And again in the passage above he says, “They shall never enter my rest.”
6 Therefore since it still remains for some to enter that rest, and since those who formerly had the good news proclaimed to them did not go in because of their disobedience, 7 God again set a certain day, calling it “Today.” This he did when a long time later he spoke through David, as in the passage already quoted:
“Today, if you hear his voice, do not harden your hearts.”[d]
8 For if Joshua had given them rest, God would not have spoken later about another day. 9 There remains, then, a Sabbath-rest for the people of God; 10 for anyone who enters God’s rest also rests from their works,[e] just as God did from his. 11 Let us, therefore, make every effort to enter that rest, so that no one will perish by following their example of disobedience.
Your question is a very good one, but it's a bit inaccurate. The Sabbath doesn't begin at 5 pm for Jews. It begins at sundown on Friday for Jews, and so it's the same for Seventh Day Adventists.
They simply follow the clear teaching in scripture regarding the Sabbath - which is also the same as Messianic Jews.
They are also much more aware and well-informed on the Jewish feasts and their significance to us as Christians, the powerful symbolism and how they all point to the Messiah.
There was a large split in the 7th Day Adventist movement or denomination and about half totally rejected the false teachings and plagairized work of Ellen White. The branch that still take her teachings is basically like a cult and they hold her writings as inspired - same level as scripture. The other group that reject Ellen White is a denomination of Christianity, like Baptists or Pentecostal.
There is nothing in scripture anywhere where God changed the Sabbath, or declared that should be moved to Sunday. This actually was just when the women went to the Tomb and he was gone, so Christians should worship on Sunday. But, the Sabbath is still on Saturday - It starts on Friday at sundown and will always be on Saturday.
Seventh Day Adventists recognize that some traditions have crept into the church but it's not what God originally commanded, so that's why they worship on the 7th day - like Jews and Messianic Jews.