Hebrews 5:7-10 meaning

Priests must give offerings to God to fulfill their priestly duties. In the days of His flesh, Christ offered up prayers and supplications (petitions) (v 7)—comparable to sacrifices offered by priests. The description With loud crying and tears (v 7) likely refers to Christ's moments on the cross when He cried out to God (Matthew 27:46); although it could also refer to Jesus's prayers in the Garden of Gethsemane before He was arrested and taken to His death (Matthew 26:36-46), as well as other instances not recorded. 

God, the One able to save Him from death (v 7), heard the cries of Jesus because of His piety (reverent submission) (v 7), and His willingness to accept God's will. Jesus was indeed saved from death; although He died, He was raised again.

Jesus is God, and yet was also a human who suffered as we do. He had to experience life as we experience it in order to become our perfect high priest. The experience of suffering as a human yet without sin made Him a perfect priest because He is now able to have compassion for us in our weakness. But He is still the perfect example of obedience, even in the face of suffering. Jesus is described here as being made perfect (v 9). 

This word perfect is the Greek word "teleo," which means "persevering until the end," or "completing the task," or "finished." The point is that Jesus worked all throughout His life to complete all that God had appointment Him to do. He was then made perfect (Greek, "teleo") since He was finished with His work.

The Pauline Author writes that although He was a Son, Jesus learned obedience from the things which He suffered (v 8). It is interesting to note that Jesus learned something. It would seem that God has nothing to learn since He is God. Jesus did not learn to be obedient as a new thing—He had been obedient as the Son in heaven from the beginning of time. But He was obedient throughout His whole life as a human, and His obedience was something that He had to learn. A major difference between heaven and earth is that on earth, God's presence is veiled.

Living on earth as an obedient human requires faith. Jesus had to learn to walk by faith, just like any of us must learn to walk by faith. Jesus did not have to have faith while in heaven—His Father was visibly with Him in all His glory. But on earth God's presence was cloaked, and Jesus had to walk by faith as a human. We have the opportunity to follow the example of Jesus who won the title "Son" as a reward for the complete obedience of walking in faith during this life (Hebrews 2:9-10). 

Jesus completed ("teleo") His work on earth walking by faith; "teleo" here is translated having been made perfect. The things He learned in His walk of faith form a part of the knowledge that makes Him a perfect ("teleo") compassionate priest for us.

Christ was made a perfect or completed ("teleo") high priest through His suffering and obedience, and He became to all those who obey Him the source of eternal salvation (v 9). 

The kind of salvation talked about here is not the salvation that makes us right before God when we initially place our trust in Him. Our justification is not contingent on our obedience to God, rather it is gained by faith in the gospel (John 3:14-15).

The eternal salvation discussed here is what the Pauline Author has been referring to in his warnings to the Hebrews: they could miss out on their inheritance if they do not walk in obedience to God all the way until they are complete ("teleo"). We can share in Christ's inheritance reward if we follow His example of obedience fully until we are finished ("teleo"). 

This eternal salvation means to be fully and completely delivered from the Fall of Man, and restored to our original design to steward the earth (Hebrews 2:5-8). This is a salvation we do not want to "neglect" (Hebrews 2:3). We gain being restored to the "glory and honor" of reigning with Christ in the earth if we also participate in the "suffering of death" with Him, by putting aside self and walking in obedience to the Spirit (Hebrews 2:9). 

Our high priest (Jesus) allows us to walk in this obedience because whatever we go through on earth, He sympathizes with, has compassion, and gives us mercy and grace to endure. Christ gave us an example, but He also empathizes with our weakness and intercedes to God for us. Through His obedience even to death on the cross, Jesus became the source of eternal salvation. It is through the "suffering of death" that He restored humanity's design and opportunity to steward over the earth (Hebrews 2:9). And He now stands designated by God as a high priest according to the order of Melchizedek (v 10) to intercede for us, that we might also learn obedience in all God has for us to learn. In learning that obedience, putting to death the self-seeking ways of the flesh, we can gain the great reward of being one of many "sons" that Jesus desires to bring to "glory" (Hebrews 2:9-10). 

Christ's priesthood being according to the order of Melchizedek is a quotation of Psalm 110:4 and will be explained in detail in Chapter 7 of Hebrews. The point here is that Christ was made a source of salvation as the high priest, designated by God. Melchizedek is a type, a foreshadowing, a representation of our high priest, Christ: a king-priest of righteousness and of peace. Jesus Christ remains our high priest forever.