C. F. Keil and Franz Delitzsch on Leviticus 8:5

Lev 8:5

When the congregation was assembled, Moses said, “This is the word which Jehovah commanded you to do.” His meaning was, the substance or essential part of the instructions in Exo 28:1 and 29:1-37, which he had published to the assembled congregation before the commencement of the act of consecration, and which are not repeated here as being already known from those chapters. The congregation had been summoned to perform this act, because Aaron and his sons were to be consecrated as priests for them, as standing mediators between them and the Lord.

After this the act of consecration commenced. It consisted of two parts: first, the consecration of the persons themselves to the office of the priesthood, by washing, clothing, and anointing (Lev 8:6-13); and secondly, the sacrificial rites, by which the persons appointed to the priestly office were inducted into the functions and prerogatives of priests (vv. 16-36).