Here is the sample space, where the left number within each
pair of parentheses represents the number rolled on the first
die and the second represents that on the second die.

(1,1) (1,2) (1,3) (1,4)

(2,1) (2,2) (2,3) (2,4)

(3,1) (3,2) (3,3) (3,4)

(4,1) (4,2) (4,3) (4,4)  

Next I will color the ones red which have a sum of 5:

(1,1) (1,2) (1,3) (1,4)

(2,1) (2,2) (2,3) (2,4)

(3,1) (3,2) (3,3) (3,4)

(4,1) (4,2) (4,3) (4,4)

That's 4 out of 16, so the probability is  which reduces to 

Edwin