Answer
5 diagonals.
Work Step by Step
We must select two vertices among five vertices. The order in which they are selected is not important. So, we have $_5C_2$ different combinations:
$_5C_2=\frac{5!}{(5-2)!~2!}=\frac{5\times4\times3!}{3!~2!}=10$
But, among those 10 combinations, five are sides.
$Diagonals=10-5=5$
