Hebrews 5:10 - Coke's Commentary on the Holy Bible

Called of God, &c.— It is not the word καλουμενος, as Hebrews 5:4 but προσαγορευθεις, having the title of high-priest given him of God the Father. He was not called to his office, as Aaron was, but he was something more; and, which shews an infinitely superior honour in this respect, he was saluted with that title by God the Father himself. Called after the order of Melchisedec means, that Christ was called to be a high-priest after the order of Melchisedech, not by having a series of successors, nor by having his title founded upon any lineal descent; but as acting in his office, without dependence upon, or attachment to any particular family.