Geometry

We can use the Law of Cosines to solve this problem. Applying it, the law states that

$AE^2 = AF^2 + FE^2 - 2 (AF * FE) cos (60°)$

Now, plugging in the values from the problem we already know, we find that

$AE^2 = 2^2 + 5^2 - 2(2* 5) (1/2)\\ AE^2 = 19\\ AE = \sqrt {19}$

Thanks! :)