Probability of Independent Events

A coin that comes up heads with probability $p > 0$ and tails with probability $1-p > 0$ independently on each flip is flipped eight times. Suppose the probability of three heads and five tails is equal to $\frac{1}{25}$ of the probability of five heads and three tails. Let $p = \frac{m}{n}$, where $m$ and $n$ are relatively prime positive integers. Find $m+n$.

Source: AIME