What is the probability of rolling a 5 or not rolling a 5 using a regular 6-sided number cube?

Well, the probability of rolling a 5 would be 1/6, the probability of not rolling a 5 would be 4/6 or 2/3.

Since the problem uses or, the question is asking for the probability of one or the other occurring, in other words the probability is more that if it were to simply be one event. Thus we add the probabilities together.

1/6 + 4/6 = 5/6.

There are 6 different sides you can land on with a dice. So the probability of rolling any one side is 1/6. The probability of NOT rolling a 5 is the same thing as rolling anything except a 5. So that probability will be 5/6.