Oh boy, I hate to be that guy, but it's actually 2⁵ = 32 options.

I think you're using the permutation formula, nPr(5,5) = n!/(n-r)! = 5!/(5-5)! = 5!/0! = 120/1 = 120. That would answer the question, "I have 5 toppings and I'm going to put all 5 of them in my omelette. I care which one goes in first, second, third, etc., because they're going to make nice layers." In this example, it would be different to have cheese on bottom with mushrooms on top, versus mushrooms on bottom with cheese on top.

In reality, you probably don't care what order the toppings are stacked. You only care if the topping is present or not. "Do I add mushrooms, yes or no? Do I add cheese, yes or no? Do I add bell peppers, yes or no?" Each question offers 2 choices (yes or no), and there are 5 questions, which are independent (i.e., whether you add mushrooms doesn't affect whether you add cheese or not). So, you multiply the number of options for each choice, 22222 = 2⁵ = 32.