I think you are saying that "dik" means something like "Given:", and "dit" means something like "Find:".

You are told that f has period 5; one implication is that if you shift the bounds of an integral by 5 (or a multiple of 5), the result is unchanged. So the integral from -5 to -4 is the same as, say, the integral from 0 to 1. Do you see that? Then, what is the integral from 0 to 5?

Then, what can you put together to get the integral from 5 to 15?

But you also need to learn to talk to your professor. That is part of how you learn, and is part of what he is paid to do!