Albert Barnes on Hebrews 5:10

Called of God. Addressed by him, or greeted by him. The Word. here used does not mean that he was appointed by God, or "called" to the office, in the sense in which we often use the word but simply that he was addressed as such, to wit, in Ps 110.

An High Priest. In the Septuagint, (Ps 110.4,) and in Heb 4:6 above, it is rendered priest -- ιερευς ---but the Hebrew word cohen--is used to denote the high priest, and may mean either. See Sept. in Lev 4:3. Whether the word priest, or high priest, be used here, does not affect the argument of the apostle.

After the order of Melchisedek. Heb 5:6.

(c) "High Priest" Heb 5:6