This gives the probability that exactly x events occurred.
So for our good friend the guessing Colin since there are 5 choices and he picks at random his probability of success is
You have also said for Colin to pass he must get at least 5 questions correct. So this means he will pass if he gets 5,6,7,8,9, or 10 questions correct. So we need to find each of these probabilities and sum them up. So here is the binomial theorem
So our answer is
This should get you started.