In this chapter, Moses again states the ten commandments and recounts his time on Mount Sinai before the LORD.
This chapter opens the stipulations section of the covenant, listing the commands that the Israelites must follow. While this chapter forms the core of the new covenant, there are still another 29 chapters in Deuteronomy, so clearly the bulk of the text still lies before us. Several major parts of Deuteronomy can be viewed as expansions on the ten commandments. I don't want to dwell on this too much here, because we have not yet reviewed Deuteronomy as a whole, but I'll give one example. Deut 19, 20 and 21:1-9 are an extended discussion of the prohibition on murder (the sixth commandment), because these passages discuss the cities of refuge (related to murder), rules of warfare (authorizing killing other people) and the atonement process in case someone is murdered but the murderer cannot be found. I will discuss all of the other correlations as we go through Deuteronomy.
I should also direct my readers to my prior commentary on Ex 20, which is the first declaration of the ten commandments. The text for nine of the commandments is virtually identical between Deut 5 and Ex 20. There is only one commandment that is worded differently, which is the command to honor the Sabbath (the fourth commandment). In Ex 20:8-11, the LORD explained the Sabbath by tying it to the seven days of creation. Here, there is no mention of the creation of the world, but rather the LORD states that it is because he freed the Israelites from Egypt. That is when the Sabbath was first given, of course, beginning in Ex 16. This is a minor variation and probably not significant. For anything else directly related to the commandments, read my commentary on Ex 20.
The second half of Deut 5 is basically Moses recounting the events of Ex 20:18-21. This is another place where Deuteronomy expands, rather than omits, from the Exodus storyline. Overall, the character of the two passages seems very similar to me, but one part I find interesting is how the LORD commends the Israelites for asking Moses to mediate between them and the LORD. He says "they have done well" because this request demonstrates that they "would fear me", i.e. have a fear of disobeying the LORD and an earnest desire to follow all his commands. I have heard some commentators suggest that the Israelites sinned by seeking to place a man between them and God, but here it is very clear that the LORD approves their request, because it demonstrates fear. Of course, it turns out the fear is short-lived, as the people rapidly descend into idolatry even before Moses returns from Mount Sinai.
This part of the chapter also serves as a transition from the "general stipulations" to the "specific stipulations". Verse 31 in particular points out that Moses is to remain so the LORD may "speak to you all the commandments and the statutes and the judgments which you shall teach [the Israelites], that they may observe them in the land which I give them to possess". What follows, therefore, is Moses recounting these more specific commandments, statutes and judgments, which serve to expand upon the ten commandments.
We can conclude that Moses is recounting what he was told on the mountain, so there should be some parallels between this and Exodus, in particular Ex 21-23, which is the equivalent stipulations section for the Exodus account of the covenant. Interestingly, Ex 21-23 also expand on the commandments, but only five, mostly concentrated in the "earthly relationships" section. Ex 21:12-35 discusses murder (6th commandment), Ex 22:1-14 discusses theft (8th commandment, not correctly ordered), Ex 22:16-31 discusses adultery (7th commandment), Ex 23:1-9 discusses false testimony (9th commandment), and Ex 23:10-19 is out of place and discusses the Sabbath (the 4th commandment).
Deuteronomy has 21 chapters (Deut 6-26) where Exodus only has 3, so clearly Deuteronomy is far more expansive. The "specific stipulations" also include sections from Leviticus, which ties the authorship of that book together with this and Exodus/Numbers (by association). Although Leviticus is crafted primarily as a priestly reference guide, its partial inclusion here in Deuteronomy should make it clear that it is indeed part of the law given by Moses and meant to be understood and obeyed by the people.
As an aside, my readers should understand that most of Israel is illiterate at this time and probably couldn't read the Pentateuch if they even had a copy. And it's unlikely they have a copy because this book had to be written and transcribed by hand, an extraordinarily laborious process. The chief method of transmission then is oral recital, which also possibly explains why there are Sabbaths and new moon festivals: it brings the people together that they might hear a recital of the law. This also shows why the priesthood is so important, because the priests would generally have authority over the written Torah scrolls.