Below are all 36 possible rolls.  The red ones are the
only ones with a 5 on either die or the sum of both dice is 5 

(1,1) (1,2) (1,3) (1,4) (1,5) (1,6)

(2,1) (2,2) (2,3) (2,4) (2,5) (2,6)
 
(3,1) (3,2) (3,3) (3,4) (3,5) (3,6) 

(4,1) (4,2) (4,3) (4,4) (4,5) (4,6)
 
(5,1) (5,2) (5,3) (5,4) (5,5) (5,6)
 
(6,1) (6,2) (6,3) (6,4) (6,5) (6,6)  

Count the red ones.  There are 15.  The probability is 15 out of 36,
or 15/36 which reduces to 5/12.

Edwin