2 Corinthians 5:17 is the reason why we obey the law (refrain from sinning, since sin is the transgression of the law) as Christians.
The law is written in our hearts and on our minds in the New Covenant (Hebrews 8:8-10, Hebrews 10:16, Romans 8:4, Romans 8:7); and therefore it governs us from the inside. The love of God is shed abroad in our hearts (Romans 5:5); and this is the fulfilling of the law (Romans 13:8-10, Romans 8:4, 1 John 5:3, 2 John 1:6).
But the law does not have any power any longer to condemn the born again believer from the outside; for he is forgiven of past, present, and future sin (Romans 4:8, Romans 8:38-39, ("things present and things to come"), Hebrews 9:12).