As Paul is explaining in Romans 5—8 the results of salvation by grace through faith, in order to show the magnificence of God’s grace, Paul first illustrates the human need for grace. We have been justified (declared righteous by God), and now we have peace with God (Romans 5:1). Before that we were helpless (Romans 5:6), and we were enemies of God (Romans 5:10). We were in bondage under sin because we were born from Adam, whose sin left a stain on all those who would follow in his line (Romans 5:12–19). As if sin wasn’t grievous enough, sin was amplified by law or ethics and rules of behavior in general (Romans 5:20) and was later amplified even further by the Law of Moses, which became a tutor to show people their need for Christ (Galatians 3:17–24). But in His grace God did not leave us in this hopeless and helpless position. While we were still helpless, Christ died for us (Romans 5:6), expressing the ultimate gift of grace and providing for our justification by faith in Him. The result is peace with God.
No longer are we enemies of God or children of wrath as we once were (Ephesians 2:1–3), because where sin abounded grace abounded more (Romans 5:20). Even when human law and the Law of Moses brought increased opportunity for sin (Romans 7:7–8), God’s grace still covered all of it through the shed blood of Jesus on the cross, because while we were yet sinners Christ died for us (Romans 5:8). Paul explains this later as the essence of the gospel—that Christ died for our sin (1 Corinthians 15:1–3). Because where sin abounded grace abounded more (Romans 5:20), we can have justification and new life through Jesus Christ by believing in Him.
Because of God’s grace expressed through the blood of Jesus poured out as a substitute for us, we are no longer in bondage to sin and are now free to live in Christ (Romans 6:6–8). This is why Paul could exclaim that he was not ashamed of the gospel—it is how God has provided for the salvation of all who believe in Jesus Christ, no matter their past (Romans 1:16–17). Where sin abounded, grace abounded more (Romans 5:20), and because of God’s abounding grace, we can now be filled with joy, peace, and hope (Romans 15:13).