Lazy Random Walk Hitting Time

A particle moves on $\{0, 1, 2, 3, 4, 5\}$. At each step from state $i$ ($0 < i < 5$), it stays at $i$ with probability $\tfrac{1}{3}$, moves to $i-1$ with probability $\tfrac{1}{3}$, and moves to $i+1$ with probability $\tfrac{1}{3}$. State $0$ is reflecting: from $0$ the particle moves to $1$ with probability $\tfrac{2}{3}$ and stays at $0$ with probability $\tfrac{1}{3}$. State $5$ is absorbing.

Starting from state $0$, derive the expected number of steps to reach state $5$.