I am sorry but your argument is flawed. The question is very clear. It says the small circle is 'rolling' completely, which means it has to rotate around it's centre forever while moving, there's absolutely no sliding motion. Then the question asks, how many 'rotations' did the small circle make, not how many 'times' the small circle had to roll completely. If the question was the latter the answer wound have been 4. But given the change in orientation of the initial position that occurs in the small circle owing to moving on the big circle, we must consider a 5th rotation!

I am sorry but your argument is flawed. The question is very clear. It says the small circle is 'rolling' completely, which means it has to rotate around it's centre forever while moving, there's absolutely no sliding motion. Then the question asks, how many 'rotations' did the small circle make, not how many 'times' the small circle had to roll completely. If the question was the latter the answer wound have been 4. But given the change in orientation of the initial position that occurs in the small circle owing to moving on the big circle, we must consider a 5th rotation!