I filed for divorce 5 years ago from my ex-husband... He signed our child's Birth Certificate and I know our son is not biologically his child. He refuses to take a paternity test and I want him out of our lives. I told him over 4 years ago that our son was not his... He still refuses to take a paternity test and my lawyer told me that it's been too long now and there is nothing I can do about it because my ex is still paying child support and seeing my son. What can I do?

I would assume your attorney is right, it varies by state ( if in the US) in some states the actual bio father can contest at any time till the child is no longer a minor, in others they can not contest at all, and in some they only have a limited time.

I respect your husband, he was there when the child was born and was there at the early time, to him the child is his and he is treating the child as his. That is what a real father does,

So no idea why you want him out of the child's life, he does not have to be in your life, you don't ever even have to see him,

As your lawyer said, there's probably nothing you can do at this point. Only a court order can compel your ex to submit to a DNA test. But look at the facts: he signed the birth certificate (which constitues a legal acknowledgement of paternity), he pays support and has visitation. Were you still married at the time of the birth? Why did you permit him to sign the birth certificate? Given the circumstances, convincing a judge to order a DNA test at this point, your chances are slim to none.