I believe you are at the passage that corresponds with the issue here.@Episkopos , @David Taylor , @John Caldwell , @Steve Owen
What did Jesus suffer that brought Him to obedience?
Hebrews 5:
6 As He also says in another place:
“You are a priest forever
According to the order of Melchizedek”;
7 who, in the days of His flesh, when He had offered up prayers and supplications, with vehement cries and tears to Him who was able to save Him from death, and was heard because of His godly fear, 8 though He was a Son, yet He learned obedience by the things which He suffered. 9 And having been perfected, He became the author of eternal salvation to all who obey Him, 10 called by God as High Priest “according to the order of Melchizedek,” 11 of whom we have much to say, and hard to explain, since you have become dull of hearing.
Hebrews 5:1-10 For every high priest taken from among men is appointed on behalf of men in things pertaining to God, in order to offer both gifts and sacrifices for sins; he can deal gently with the ignorant and misguided, since he himself also is beset with weakness; and because of it he is obligated to offer sacrifices for sins, as for the people, so also for himself. And no one takes the honor to himself, but receives it when he is called by God, even as Aaron was. 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.
I believe Christ had to suffer in terms of "chastening", of bearing our sorrows and griefs. He had to be made like us in every way, yet without sin. He had to be pierced through for our transgressions and crushed for our iniquities and experience death as the wages of sin NOT because He was a sinner but because He was made like us in every way (He was human). Therefore He can be a High Priest (OUR High Priest). He is the Firstborn. He is the Second Adam. I believe this is what Isaiah 53 is directing us to. He became a curse for us and by His stripes we are healed and escape the wrath to come.
What Christ suffered was abuse and murder Scripture speaks of as evil performed by wicked men but by the predetermined plan of God. These men could be forgiven because the evil they did was in ignorance. (see Peter's sermon in Acts).
But I do not believe God was punishing Jesus on the cross. Scripture teaches that Jesus is righteous and it is an abomination to God to condemn the righteous and that the righteous are objects of God's chastening but NOT His wrath.