AHSME 1995 Problem 20

If $a,b$ and $c$ are three (not necessarily different) numbers chosen randomly and with replacement from the set $\{1,2,3,4,5 \}$, the probability that $ab + c$ is even is

$\mathrm{(A) \ \frac {2}{5} } \mathrm{(B) \ \frac {59}{125} } \mathrm{(C) \ \frac {1}{2} } \mathrm{(D) \ \frac {64}{125} } \mathrm{(E) \ \frac {3}{5} }$