So also Christ did not glorify Himself so as to become a high priest, but He who said to Him, You are My Son, Today I have begotten You; just as He says also in another passage, You are a priest forever According to the order of Melchizedek. In the days of His flesh, He offered up both prayers and supplications with loud crying and tears to the One able to save Him from death, and He was heard because of His piety. Although He was a Son, He learned obedience from the things which He suffered. And having been made perfect, He became to all those who obey Him the source of eternal salvation, being designated by God as a high priest according to the order of Melchizedek. - Hebrews 5:5-10
First, like Aaron, Jesus was appointed by God to be a High Priest. The phrase so also Christ compares Jesus’ High Priestly appointment to that of Aaron’s. Christ did not glorify Himself means that the High Priestly office was not something that Jesus sought for Himself. Paul quotes Psalm 2:7 — You are My Son, Today I have begotten You -- to remind the reader that Jesus became a priest at His resurrection. Today refers to the day Christ was enthroned. He then quotes Psalm 110:4 — You are a priest forever according to the order of Melchizedek — to show that God the Father appointed Jesus before His incarnation to be a priest forever. Jesus is designated (prosagoreúō) or given the title, High Priest, by God.