For the sum of the two dice to be greater than 8, given that the first die is a 5,
you can either roll a 4 OR 5 OR 6.
Therefore, the Probability of rolling a 4 OR 5 OR 6 =
[tex]\frac{1}{6}\text{ + }\frac{1}{6}\text{ + }\frac{1}{6}\text{ = }\frac{3}{6}\text{ = }\frac{1}{2}[/tex]Thanks!