Double Step Particle II

Fix $0 < p < 1$ . A particle performs an asymmetric random walk on the integers. The particle starts at position $k > 0$ . Each turn, the particle moves from position $k$ to positions $k+2$ or $k-1$ with respective probabilities $p$ and $1-p$ , independent of previous turns. Find the probability that the particle ever hits the origin when $p = 1/2$ and $k = 5$ . Round to the nearest hundredth.

Answer format: round to 2 decimal places.