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)