random variables - How many students would have to take the exam to ensure with probability at least $.9$ that the class average would be within $5$ of $75$?

I'm having trouble solving this problem:

From past experience, a professor knows that the test score of a

student taking her final examination is a random variable with mean
$75$.
How many students would have to take the examination to ensure with
probability at least $.9$ that the class average would be within $5$ of
$75$? Use the central limit theorem.

The professor knows that the variance of a student's test score is $25$.

I'm not entirely sure on how to solve this problem.

Right now this is what I have:

We know: $\mu = 75$ and $\sigma^2 = 25$.

This is what I set up (by defn C.L.T): $\mathbb{P}(\frac{X_1+\cdots+X_n - n75}{5\sqrt{n}}\le\frac{.9-n75}{5\sqrt{n}}) = 1-\mathbb{P}(\frac{X_1+\cdots+X_n - n75}{5\sqrt{n}}>\frac{.9-n75}{5\sqrt{n}})$

I'm not sure how to solve for $n$. Thanks.