5 In the same way, Christ did not take on himself the glory of becoming a high priest. But God said to him, “You are my Son; today I have become your Father.”a

Read Hebrews 5:5 Using Other Translations

So also Christ glorified not himself to be made an high priest; but he that said unto him, Thou art my Son, to day have I begotten thee.
So also Christ did not exalt himself to be made a high priest, but was appointed by him who said to him, "You are my Son, today I have begotten you";
That is why Christ did not honor himself by assuming he could become High Priest. No, he was chosen by God, who said to him, “You are my Son. Today I have become your Father. ”