We get our modern English versions of the New Testament from 1000s of very early Greek manuscripts. The Greek word for peace in Romans 5:1 means "to glue together that which has been separated." And the Greek word for with that precedes this word peace means "face to face."
Wow! Do you realize how intricate God's Word is in describing what He has done for and in you?! The Holy Spirit wants us to know the intricate and beautiful details of our intimate and beautiful relationship with Christ!
THE GIFT OF RIGHTEOUSNESS
You see, everyone is born an enemy of God. When God saved us, it was not merely a transaction for reconciliation, but was a transformation for relationship!
We were justified means that we were not only "forgiven' but we were "made righteous" with the righteousness of Christ! This righteousness is a gift. It cannot be earned. It can only be received by faith as noted in Romans 5:1.
Righteousness is our birthright as a child of God, although we do not always choose to live out of this foundational righteousness and true identity.
THE GIFT OF RELATIONSHIP
It is only because of this amazing transformation into the righteousness of Christ that we can have an intimate relationship with holy God!
So the phrase in Romans 5:1 we have peace with God means that God has transformed us into His righteous children so that He could turn each one of us to look right into His loving face without any fear of condemnation...and so that He could glue each one of us to be one with His dear Son so that we now have His character that we can learn to grow in living out of.
Through this relationship, God is revealing the glory of His Son to the world through us!