Bold Play to Five Tokens

You hold 3 tokens and want to reach 5 before hitting 0. Every bet pays even money: you stake $s$ tokens, you win $s$ more with probability 1/4, and you lose the stake with probability 3/4. Bets are independent.

You play bold: on each bet you stake as much as you can without overshooting the target, that is $\min(x, 5-x)$ tokens when you hold $x$.

What is the probability that you reach 5 before going broke? Answer format: round to 3 decimal places.