Poisson mode from a probability ratio

Let $X$ be a random variable having Poisson distribution with mean $\lambda > 0$ such that $P(X = 4) = 2 P(X = 5)$. If $p_k = P(X = k)$, $k = 0,1,2,…$, and $p_\alpha = \max_k p_k$, then $\alpha$ equals ________ (in integer).