1995 AIME Problem 15

Let p_{} be the probability that, in the process of repeatedly flipping a fair coin, one will encounter a run of 5 heads before one encounters a run of 2 tails. Given that p_{} can be written in the form m/n where m_{} and n_{} are relatively prime positive integers, find m+n.

Leading zeroes must be inputted, so if your answer is 34, then input 034

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.