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 \(m+n\).
(第十三届AIME1995 第15题)