Legal Question in Family Law in Texas

You can't just refuse to testify (well, you could, but the judge could hold you in contempt for your refusal, and presumably you don't want to go to jail over this). You can decline to answer the question only based on some specific privilege (doctor-patient, confessor-penitent, lawyer-client, etc.), or because your answer might tend to incriminate you. The last one is all the protection the Fifth Amendment provides (it isn't the catch-all solution for any question you just don't feel like getting into due to privacy issues or whatever), and it's not absolute. Among other things, it's subject to a common-sense inquiry of whether the subject area is one that could possibly involve information of that sort.