What does Romans 1:5 mean?
After declaring who Jesus is—both man and Son of God, resurrected from the dead and deserving of the title "Our Lord"—Paul returns to identifying himself to his readers. It turns out that Paul's identity cannot be separated from that of Jesus.It is through Jesus that Paul has received grace, which is unearned favor, as well as apostleship, which gives Paul the authority to speak on Christ's behalf. Paul has been sent by Christ, for the sake of Christ's name—or for the sake of His honor—to bring about the "obedience of faith."
That's a very specific phrase. Paul will be completely clear about what this does not mean. He has not been sent by Christ to get people to obey the law of Moses. He has been sent to bring about obedience to faith in Christ. In other words, Christ calls people to believe in Him. To refuse to believe in Jesus is to disobey that call. Believing is obedience, both in becoming a Christian and walking in Christ throughout our lives.
Paul has been sent to bring this about among "all the nations." Paul's unique mission, given to him directly by Jesus, was to carry the good news about salvation through faith in Christ to all the non-Jewish peoples of the world.
Here's what Jesus said about Paul in Acts 9:15: "He is a chosen instrument of mine to carry my name before the Gentiles and kings and the children of Israel."