Albert Barnes Commentary Psalms 78:5

"For he established a testimony in Jacob, And appointed a law in Israel, Which he commanded our fathers, That they should make them known to their children;" — Psalms 78:5 (ASV)

For he established a testimony in Jacob — He ordained or appointed that which would be for a “witness” for him; that which would bear testimony to his character and perfections; that which would serve to remind them of what he was, and of his authority over them. Any law or ordinance of God is thus a standing and permanent witness regarding his character, showing what he is.

And appointed a law in Israel — That is, He gave law to Israel, or to the Hebrew people. Their laws were not human enactments, but were the appointments of God.

Which he commanded our fathers ... — He made it a law of the land that these testimonies should be preserved and faithfully transmitted to future times. See (Deuteronomy 4:9; Deuteronomy 6:7; Deuteronomy 11:19). They were not given for themselves only, but for the benefit of distant generations also.