Psalm 72 says David's prayers are ended, and eighteen more David psalms follow

Psalm 72 ends with a line that belongs to no psalm: "This ends the prayers by David, the son of Jesse." It comes straight after a closing blessing and a double "Amen," and it reads like the last line of a book. Then the Psalter keeps going for seventy-eight more psalms, and eighteen of them carry the heading "by David."

Most scholars read the line as a scribe's closing note for an earlier collection of David's prayers, kept in place when later collections were added after it. The Psalter preserves other traces of the same assembly. It is divided into five books, and the first four each end with a short blessing and "Amen": at Psalms 41, 72, 89 and 106. Psalms 14 and 53 are nearly the same poem, copied into two different collections; where Psalm 14 uses the divine name YHWH, printed "Yahweh" in the World English Bible, Psalm 53 has Elohim, "God."

The five-book shape itself may be deliberate. An ancient Jewish commentary on the Psalms, the Midrash Tehillim, says that Moses gave Israel the five books of the Torah and David gave Israel the five books of Psalms. The collection grew over centuries, and the editors who combined its collections did not hide where one ended, including a closing note for a collection that kept growing after it was written.