One of the gifts that Jesus provided is justification (from Jesus's righteousness) in spite of our big screw-ups and going against God (AKA being an "enemy"). In particular, we are "justified by His blood" (5:9). Jesus can be considered taking on our sin's effects (rather than us) during the crucifixion. Basically a substitute. (which is basically substitution and the "great exchange").
This "great exchange" is often considered to meet the fulfillment of atonement (payment), especially as per Hebrew Law. But there are also other considerations, like how the resurrection overpowers the penalty of death. Also, blood has been used to represent life, and Jesus officially declared that the blood represents the new covenant of grace with us (as seen in Luke 22:20). The crucifixion marked the beginning of said new covenant (especially since Jesus's blood was poured out and how Jesus's covenant is like a will). Finally, the sacrificial love (Jesus's intent throughout life showcased in his will to demonstrate the power over death on behalf of us) deemed Jesus fit to provide righteousness that is the basis of our justification due to the fulfillment of the expression of God's character (and meeting God's standards in the first place). All these things are factors on how we are "reconciled to God through the death of His Son" (5:10), and justification plays a big role in that mechanism of reconciliation.
Additionally, we are also "saved from wrath through Him" (5:9). Now in the original Greek, the word for God isn't in that verse, so "wrath" is at the least a very icky scenario (whether from the world or the downfall of sin or the devil). Still, as seen in MANY translations, it's implied that Paul is describing God's wrath, and no surprise with the discourse back in Romans 1. God's wrath is basically his passion against injustices that ruin lives, and the Spirit (which we get to have) that counters injustices is good in God's eyes. Regardless, the righteousness provisions (especially from the substitution model) and justification plan cleared us of our screw-ups that result in a bad report. The Holy Spirit also fosters righteous living and ultimately frees us of sin by the time heaven begins.
And finally, we are "saved by His life" (5:10). The resurrection demonstrates that Jesus overpowers death, and Jesus offers His Spirit to us. As a result, we can "rejoice in God through our Lord Jesus Christ" (5:11). Partly because he provides a lot -- justification, His righteous Spirit, peace, hope, and reconciliation.