Also, I offer this psuedo-mathy explanation as an alternative to the more intuitive solution:
Considering the rolls as a function:
Domain {five dice, each numbered 1 to 6}
Range {0,2,4,...,12}
Solution
Substitue the following values:
evens -> 0
1 -> 0
3 -> 2
5 -> 4
Sum the substitued values.
