The guidebook says that during exams (May) many of the sights in Cambridge are closed...would it still be worth going or should we wait until June?
We went to Cambridge in May several years ago without knowing it was exam period. It was a very disappointing experience to see not a single college. Could not see any buildings and not even a quick photo of any of them was allowed. So our day was spent walking the streets and having lunch at a pub. OTOH, on another trip we went to Oxford and had a great time-loved every minute of it. So I would advise against it.
Walking around Cambridge anytime is terrific the architecture and museums are wonderful as is the river.
Go for sure.