Does a regular expression exist for any number that contains no more than two 5s and no 6 twice in a row?


For example, a valid number would be 6165156 and an invalid number would be 1566515.

I have tried many times to construct a finite state machine for this with no success, which leads me to believe the language is not regular. However, I am unsure how to formally prove this if that is indeed the case. I tried applying the pumping lemma but I am not completely sure how to apply it to this particular language.

Any help is appreciated!