"Peace with God"

In Romans 5:1 Paul says, "Therefore, since we have been justified by faith, we have peace with God through our Lord Jesus Christ."

Therefore, - Paul in previous chapters spent describing how we sinners have been set right with God. So, now the conclusion on the justification by faith.

since we have been justified by faith, - legal term "justified" means 'pronounced not guilty / but pronounced right, righteous'. And that justification, is not by faith in general, or in the existence of God, but specifically faith in Christ Jesus, as it relates to his death in the place of us sinners.

we have peace with God - and "peace with God" is the result of such justification by faith. These words of Paul imply that "we" by nature are at war with God, and God with us, until we come to have faith in Christ who died in our place. At the cross God's wrath was put upon Jesus, and now by faith in Jesus we are reconciled with God, and there is peace. Or, let us make sure to come to peace with God, by faith in Jesus, who died in our place.

through our Lord Jesus Christ. - Jesus is the only mediator between God and sinful people. His death in our place, which is substitution, is the only means of peace with God, which we can partake only through receiving him - putting our faith in Jesus - he died for me that i wouldn't have to.