How would you use it in the negative?It is just about possible to say that "five years have passed since this law existed", but really with "since" we expect an action (such as "was abolished"), not a state.
If you need to use the verb "exist", then I suggest you use it in the negative, and you don't use "since".
I think "existed" is the wrong word. "Or" is definitely wrong. There could be 50 years between:Five years have passed since this law was proposed or really existed.