What is the legality of this horror?

When I was in the Navy I had 100% health care coverage through Tricare and my wife at the time was covered under the policy. She was going to doctors and getting treatment a lot. In May we separated and then in July I was discharged. I returned to my home state and proceeded to file for divorce. We have now been divorced for a couple of months. Today I received a letter in the mail from a law office in the state of our residence (back then) stating that I owe a medical center $5,000 and that it is an attempt to collect a debt. I have a sickening feeling in my gut telling me that this is hurting my credit and that I cannot do anything about it. How do I fix damaged credit from something like this and is it even legal for them to report on MY credit report? She was the one getting treatment and failed to tell tricare about it. I had no knowledge of this until now, now that I'm divorced! O did I forget to mention that she currently has no job and no way to pay it off which leads me to believe that if we are both liable, she can't pay, I'm not going to pay it will continue to hurt my credit. Is this true?