David has a coin that lands heads with probability $\frac{1}{5}$, and Emily has a coin that lands on heads with probability $\frac{1}{4}$. David and Emily alternately toss their coins until someone gets a head; the first one to get a head wins. All coin tosses are independent. Emily goes first. The probability that David wins is $\frac{p}{q}$ where $p$ and $q$ are relatively prime positive integers. What is $q-p$?