Roll it again!

For a sum of 5 either 3,2 2,3 4,1 1,4 will appear and for a sum of 7 either 5,2 2,5 4,3 3,4 6,1 1,6 will appear. So, total no. of outcomes are 10 and 5 can appear in 4 ways. Hence, Probability of 5 coming before 7 is 4/10=0.4

This can be solved in a generic and complex way but let us not go into all that. There can be four ways through which the pair of dice results in a sum of 5. There can be six ways through which the pair of dice can result in a sum of 7. Now, we want the probability of the pair of dice resulting in a sum of 5 before a sum of 7. Thus probability = 4/(4+6) = 4/10 or 2/5 or 0.4