> I figured the answer must be four revolutions. So imagine my surprise when I saw that the answer was given to be five!

The answer is four from the reference frame of the small moving circle (the fifth rotation belongs now to the big circle). Imagine two circles fixed and both rotating together, like connected gears. The question is fun but only surprising because it’s ambiguous and assuming a specific reference frame without saying it (which would be a clue to what’s really being asked.)