Gambler's Ruin with Stochastic Resetting

A gambler plays on $\{0, 1, 2, 3, 4, 5\}$ with absorbing barriers at $0$ and $5$. At each step from transient state $k$, with probability $r = 1/4$ the gambler is "reset" to state $3$ (regardless of current position), and with probability $3/4$ she takes a fair step ($+1$ or $-1$ each with probability $3/8$). Starting from state $2$, find the probability of reaching $5$ before $0$.