Sample Size for Desired Estimation Accuracy

A random variable $X$ has mean $\mu = 5$ and standard deviation $\sigma = 2$. You observe $n$ independent copies $X_1, \ldots, X_n$ and compute $\bar{X}_n$.

Using the CLT, find the smallest $n$ such that $P(|\bar{X}_n - 5| > 0.3) < 0.05$.

You may use $\Phi(1.96) \approx 0.975$.