Here is my translation of Chapter 5--
"Therefore, since we have been declared to be in the right through faith, we have peace with God through our King Jesus the deliverer and high priest, through whom we have been granted access by faith into this sphere of grace in which we now stand. And we proclaim our confidence in the hope of the glory of God. Not only this, but we also remain confident in our suffering because we know that this suffering will toughen us up and make us soldiers filled with confidence in God's battle plans and this confidence will not disappoint us because God has empowered us with His selflessness by way of the Holy Spirit whom He sent. You see, just at the right time, when were morally weak, our King died for his own enemies. Very rarely will anyone die for a just man, though for a good man someone might possibly dare to die, but God demonstrates His own love for us in this--while were still in rebellion against Him, our King died for us. Since we have been absolved of punishment by his blood, how much more shall we be delivered from God's just anger through our King! For if, when we were God's enemies, we were reconciled to him through the death of His son, how much more, having been reconciled, shall we be saved through his life! Not only is this so, but we also testify in God through our King Jesus the deliverer and high priest through whom we have now received reconciliation.
Moreover, just as sin entered the world through one man, and death through that sin to all persons, because all sinned, indeed, remember, that even before the Mosaic law was handed down, sin was in the world, but sin was not counted as sin because there was not law yet to break! Yet, everyone died--from the time of Adam to the time of Moses--even those who did not disobey an explicit commandment of God, as Adam did. Now Adam was a model of what was to come. Yet the redemptive gift is not the same as the death inducing sin. If one man's rebellion against God pushed innumerable persons into the realm of death, just think what God's unmerited gift poured out in the one man, Jesus the King, will do! Again, the gift of God is not like the product of one man's sin against God--judgment followed that one sin but the gift follows many sins and brings reconciliation with God.
For, if the rebellion of one man, Adam, death reigned, how much more will those who receive God's wonderful gift of grace and reconciliation live in triumph over sin and death thanks to one man--King Jesus.
Yes, Adam's one sin brought condemnation for everyone but our King's one act of justice brings reconciliation with God and new life for everyone. Because one person disobeyed God, many became rebellious but because one person obeyed God, many will be reconciled.
God's law was given so that all people could see how sinful they are but people just sinned more and more, yet God's wonderful grace multiplied. So, just as sin ruled over all people and brought them death, now God's wonderful grace reigns instead, giving us right standing with God and resulting in eternal life through Jesus our King, deliverer and high priest.