There are 13 sets of 4 cards in a deck of card. So, there are 13 ways to get four cards of the same face value. The next card you pick will always be a different face value. So, essentially, you have 13 x 48 combinations of 5 cards that you can pick from the deck where you have 4 cards of the same face value and 1 card of a different face value.
13 x 48 = 624.
