Romans 10:4-5 — For Christ is the end of the law for righteousness to every one that believeth.
For Moses describeth the righteousness which is of the law, That the man which doeth those things shall live by them.
end = when something is no longer what it was until then
The law is no longer in dominion — But before faith came, we were kept under the law, shut up unto the faith which should afterwards be revealed. Wherefore the law was our schoolmaster to bring us unto Christ, that we might be justified by faith. But after that faith is come, we are no longer under a schoolmaster. For ye are all the children of God by faith in Christ Jesus (Romans 10:4-5).
Moses' quote — Ye shall therefore keep My statutes, and My judgments: which if a man do, he shall live in them: I am the LORD (Leviticus 18:5). Cursed be he that confirmeth not all the words of this law to do them. And all the people shall say, Amen (Deuteronomy 27:26).
doeth = has done. Once a man determines to gain his righteousness by law, he can never fall short of the standard.
Christ was the fulfillment and the termination of the law.
He was the goal — Wherefore the law was our schoolmaster to bring us unto Christ, that we might be justified by faith (Galatians 3:24).
He ended it — But after that faith is come, we are no longer under a schoolmaster (Galatians 3:25).
Having abolished in His flesh the enmity, even the law of commandments contained in ordinances; for to make in Himself of twain one new man, so making peace (Galatians 2:15).
Blotting out the handwriting of ordinances that was against us, which was contrary to us, and took it out of the way, nailing it to His cross (Colossians 2:14).
Efforts to keep the Law will never establish one's righteousness; rather they will establish his unrighteousness. God's righteousness, required by the Law, was manifested in Christ alone, in whom our sins were judged at Calvary, by whom their penalty was fully paid, and through whom we may now be justified by faith. This is why Paul declares that it is his desire to be found in Him, not having mine own righteousness, which is of the law, but that which is through the faith of Christ, the righteousness which is of God by faith (Philippians 3:9). — C.R. Stam, The Epistle of Paul to the Romans, page 241.