A die is rolled 5 times, and let $a$ be the number of times an odd number appears. A coin is tossed 4 times, and let $b$ be the number of times heads appears. If the probability that $a - b = 3$ is $\frac { q } { p }$, find the value of $p + q$. (Here, $p$ and $q$ are coprime natural numbers.) [3 points]