Probability of getting at most 2 hearts in a 5 card hand, using a normal 52 cards deck?

Question

I think I know how to do it, but I am not 100% sure and also maybe there is a better way of doing it.

My solution

$$\binom{13}{0} \times \space \binom{39}{5} + \binom{13}{1} \times \space \binom{39}{4} + \binom{13}{2} \times \space \binom{39}{3}$$