The righteousness that come from the law is one thing according to verse 5; the righteousness that comes from faith is something else, according to verse 6-8. But, this is not an argument about which is superior--Judaism or Christianity, because both arguments come from what Christians call the Old Testament. Jewish arguments presented for an aid to understanding Christianity?
Righteousness from the law: see Leviticus 18:5, You shall keep my statues and my ordinances; by doing so one shall live: I am the Lord.
Righteousness is not something human beings are capable of achieving on their own. God's help is necessary: see Deuteronomy 30:11-14, Surely, this commandment that I am commanding you today is not too hard for you, nor is it too far away. It is not in heaven, that you should say, "Who will go up to heaven for us, and get it for us so that we may hear it and observe it?" Neither is it beyond the sea, that you should say, "Who will cross to the other side of the sea for us, and get it for us so that we may hear it and observe it? No, the word is very near to you; it is in your mouth and in your heart for you to observe.