Three-Outcome Random Walk to Absorption

A particle moves on $\{-5, -4, \ldots, 4, 5\}$ with absorbing barriers at $-5$ and $5$. At each step, the particle moves $+1$ with probability $p = 0.3$, stays put with probability $s = 0.2$, and moves $-1$ with probability $q = 0.5$. Starting from position $1$, what is the probability that the particle is absorbed at $+5$?