Absorption with a Long-Range Jump

A particle moves on $\{0, 1, 2, 3, 4, 5\}$ with absorbing states $0$ and $5$. The transitions from transient states are:

• From $1$: to $0$ w.p. $1/2$, to $2$ w.p. $1/2$.
• From $2$: to $1$ w.p. $1/3$, to $3$ w.p. $1/3$, to $4$ w.p. $1/3$ (a long-range jump).
• From $3$: to $2$ w.p. $1/2$, to $4$ w.p. $1/2$.
• From $4$: to $3$ w.p. $1/2$, to $5$ w.p. $1/2$.

Starting from state $2$, what is the probability of being absorbed at $5$?