The sandwich shop offers combo meals with a choice of one sandwich, one side, and one drink. on total there are 560 combos available. if there are 16 sandwiches and 5 drinks available, how many sides are there?

There are 7 sides available.

The fundamental counting principal tells us to find the total number of combinations of independent items, multiply the number of choices from each one (choices x choices x)

This means that drink x sides x sandwiches = 560.  We know there are 16 sandwiches and 5 drinks.  Let S be the number of sides:
15(6)(S) = 560
80S = 560

Divide both sides by 80:
80S = 560/80
S = 7