In Galatians 5:5 it tells us that those that are free live by faith through the Spirit. This shows us that we are to accept righteousness by faith through Christ, not by the works of ourselves. We are to point to the work that Christ did. The Judaizers on the other hand practice works so that they may obtain righteousness, which is something that will never end because it can not be obtained. Darrin Patrick described this well when he said, "You are under the law and not grace when you take your moral performance and offer it as your reason for salvation, this is your flesh, and you need to kill it!"
This entire passage points to the fact that we are free because Christ has made us free. We live through the power of the Holy Spirit working in and through our lives. We often recognize that the Bible teaches this, but we often communicate to God that we know better than Him and in essence communicate that we should be God.
We all have an internal problem of rebellion, sin, that no list of rules can help. It might help us look a little more moral and orderly for a time, but the reality is that we will still be walking aimlessly with no hope of salvation. But the good news is that Christ has made a way for us and our freedom in his life, death, and resurrection. And if you are attempting to mix the law and grace then you need to stop, repent, and turn to Jesus!
In turning to Jesus and away from sin, we see that you are made free. What verse 5 shows us is that although we are not righteous in our salvation, Christ's righteousness is given to us and we are now looked at as righteous. And what we are eagerly waiting for here is that even though we have received his righteousness we are waiting through faith for the completed righteousness that we will receive when we no longer battle with our flesh.
In closing, Paul shows us here that he is not one sided. It is not that he is against circumcision and for non-circumcision, but rather that he is all for Jesus as the way to salvation and nothing else. He basically says for the Gentiles not to boast in their un-circumcision and for the Jews not to boast in their circumcision because in the eyes of Christ both are irrelevant in terms of salvation.
So what might you be trying to mix with grace as means to your salvation? Or what might you be boasting in that is irrelevant in regards to salvation? Because whatever it is it is irrelevant and will never work, because as this passage shows us that salvation is in Christ Alone!