What could cause an elderly cat to become wobbly?

Have her checked by the vet. She could have an ear infection, sore joints, or vestibular disease (often from an ear infection). Only the vet can tell what is wrong. Actually, in people years, she is about 60, so she still has a few good years left. Go to the vet because often, a problem nipped in the bud is much easier to take care of, than something left to get worse. Ear infections are a good example of this. Additionally, 5 lbs, is pretty light for a cat, so she probably should be seen. Something does not sound like it is going right for her to be so light. Our cat was about 4 lbs. when she was pretty sick. Take her in.