In his introduction to the Old Testament, Lasor says that the five books of the Psalter correspond to the five books of the Pentateuch. In fact that number of psalms (150) is probably related to the sections the Pentateuch is divided into for readings in the synagogue (153). (p. 430)
Don’t remember where I came across this, but someone suggested that the Psalms breaks down this-a-way:
Book 1: Saul’s Pursuit of David
2: David’s Kingship
3: The Assyrian Crisis
4: Fall of Jerusalem and Exodus life
5: Restoration and re-establishment of Temple worship.
Seems more convincing to me than the Pentateuchal model. Just a thought. Cheers,