Infinite Rolling of Coins

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 \(\frac{m}{n},\) where \(m\) and \(n\) are relatively prime positive integers, find \(m + n.\)

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