Survival odds on a plank with sharks at one end

A blindfolded person stands on a plank $5$ metres long, at an integer number $x$ of metres from the end over the sharks (so $0<x<5$). Each step moves them exactly $1$ metre towards one end or the other, with equal probability. Stepping off the shark end is fatal; stepping off the other end lands them safely on the ship. What is the probability they survive, as a function of $x$?

$x/5$. This is the symmetric gambler's ruin: the survival probability $s(x)$ satisfies $s(x)=\tfrac12s(x-1)+\tfrac12s(x+1)$ with $s(0)=0$ and $s(5)=1$, so it is linear in $x$. Equivalently, the position is a martingale.