Romans 5 ends with the comparison between the 1st Adam and the 2nd Adam, Jesus. Just as Christ was greater in every way than Adam, so His gift is greater in every way than Adam's 'gift', which was death. Paul then goes onto counter the claims that we should continue in sin so that grace may abound. And he does this by talking about Christ rising from the dead. In 6:4 Paul says 'we were buried with Him therefore by baptism into death, so that, just as Christ was raised from that dead by the glory of the Father we too might walk in newness of life'.
Why don't we sin so that grace might abound? Because of the resurrection. Because we were baptised into Christ's death 'in order that' we too might walk in newness of life. This is stunning. Paul doesn't start with the wages of sin being death, he starts with the positive, he starts with the obvious implication of the empty tomb. If we've been dead like Jesus, we should be alive like Jesus.
But there's more. In verse 5 Paul says we shall 'certainly be united with Him, in a resurrection like His.' Our old self has been crucified, we've been set free from sin because Christ died on the sin. As Jesus, our substitute died for sin on the cross, we died to it. When He rose death no longer had dominion over us, because he was dead to sin. Jesus has done this, so we are to consider ourselves dead to sin, and alive to God in Him. Because He rose.
Paul finishes up this section of his though in 6:12-23. Don't let sin reign in your bodies. He rose and was dead to it, so you must count yourself as such. And the implication is that we are slaves to God. Sounds harsh but it's only right. Once we were slaves to sin, we went where sin called, for as long as sin wanted. Now we're slaves to God. Because Jesus is risen, and we live that new life with Him, we are slaves to God.
On the cross Jesus was punished for our sins. He died for our trespasses. He died that we might worship God. Jesus walked out of His tomb for our justification. (4:25) So that we could live a life free from the chains of sin and alive to God. Christ rose to buy us new life, to give us new life. So that we might not only be forgiven but justified. Just as he not only died, but also rose...