combinatorics - You are dealt five cards from a standard deck. What is the probability that you'll have at most three kings in your hand?

You are dealt five cards from a standard and shuffled deck of playing cards. Note that a standard deck has 52 cards and four of those are kings. What is the probability that you'll have at most three kings in your hand?

I know that the answer is $\frac{54144}{54145}$ from the answer key, and I know that the sample space is ${^{52}\mathrm C_5}$. What I don't get is how to find the event.

Do I just add the combination for each number of kings together (${^5\mathrm C_2} + {^5\mathrm C_3}$)?

Or do I need to multiply as well to account for the other cards in the 5-card hand?