247.Ruined on Schedule

A gambler starts with $\$n$, where $n \ge 1$ is an integer. Each round, the gambler wins or loses $\$1$ with respective probabilities $p$ and $1-p$. Once the gambler has $\$0$ left, he leaves the table. The probability that the gambler is ruined after exactly $n + 2k$ rounds ($k \ge 0$ an integer) can be written as a function $f(p, n, k)$. Compute $f(1/3,\ 5,\ 3)$ to the nearest ten-thousandth.