Answer
80 cups.
Work Step by Step
5 gal = c
Use the unit fraction $\frac{4 quarts}{1 gal}$ to change gallon to quarts, next use the unit fraction $\frac{2 pint}{1 quart}$ to change quart to pint and last use the unit fraction $\frac{2 cup}{1 pint}$ to change pint to cup. Notice how all the units divide out except cup, which is the unit you want in the answer.
5 gal * $\frac{4 quarts}{1 gal}$ * $\frac{2 pint}{1 quart}$* $\frac{2 cup}{1 pint}$= 80 cups.