When God called you to Christ, He also called you away from bondage to law. Before you trusted Christ, you were bound to God's law the way a condemned man bound to the anchor that is dragging him to the bottom of the sea is bound to die. See Romans 7:1-8.
Paul's language of bondage-to-law does not mean "the obligation to think and act in a godly way." All Christians are always obligated to do right. We have not been freed from moral obligations to man and God. The issue is, which obligations, and more importantly, why do we keep them?
No, when Paul says "bound by law", he means obligated to any and every aspect of Moses' law for everlasting life. This includes all ten of the Ten Commandments. Only Jesus Christ's death on the cross can free you. He lived the only perfect human life, then died the only satisfactory human death, on behalf of all sinners. He left absolutely nothing more for you to do, to inherit everlasting life.
Christ's death means you are freed from the whole Law -- not just the ceremonial laws like circumcision or the festivals, but every part of the law, including the Ten Commandments. You do not need to keep any of the law to receive everlasting life, or to be God's child. This idea is baffling to every legalist -- Protestant or Catholic, Muslim or Jew. But it is the Good News of Christ.
Now, Paul (anticipating obvious objections), says that God didn't give you this freedom from the Law as an opportunity to indulge your sins. Instead, Paul commands us to love one another (v. 13-14). Here again we see how Paul distinguishes between:
The failure to see these two distinctions cause great confusion between denominations. The traditional Reformed churches do not adequately distinguish between Moses Covenant and the New Covenant of our salvation. They lump the two together, as equal manifestations of the covenant of grace. As a result, they unintentionally taint the liberty of the New Covenant with Jewish legalism.
On the other hand, some dispensational churches will not acknowledge that a text like Galatians 5:13 is a commandment. They are allergic to even the word "commandment." They have confused this being the age of grace with the false idea that the New testament issues no commandments. This was the theology-of-lawlessness taught to me by "Darbyites", when I was a Christian youth.
What is Paul saying? Moses' Covenant was fulfilled by the cross, and ended by the cross. Moses' Covenant ceased. It was replaced -- not augmented or fulfilled, but replaced -- by the New Covenant in Christ's blood. This New Covenant also teaches us moral commandments, but we obey them out of life, not for life.
Paul is keeping the Biblical balance. You are free from Moses' system, but not free to sin.