Tightest Moment Bound on a Tail Probability

A positive random variable $X$ satisfies $E[X] = 1$ and $E[X^2] = 3$. Using only these two moments: 1. Find the tightest possible upper bound on $P(X \geq 5)$. State which inequality you used. 2. Construct (or describe) a distribution on $[0, \infty)$ that achieves the bound, proving it is tight.