Albert Barnes Commentary Hebrews 5:10

"named of God a high priest after the order of Melchizedek." — Hebrews 5:10 (ASV)

Called of God. Addressed by Him, or greeted by Him. The word used here 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, namely, in Psalm 110.

An High Priest. In the Septuagint (Psalms 110:4) and in Hebrews 4:6 above, it is rendered priest—iereuv—but the Hebrew word cohen is used to denote the high priest and may mean either. See the Septuagint in Leviticus 4:3. Whether the word priest or high priest is used here does not affect the argument of the apostle.

After the order of Melchisedek. See Barnes on Hebrews 5:6.