We first choose the rank of the four cards in any of these 13 ways,
{Ace,2,3,4,5,6,7,8,9,10,Jack,Queen,King}.
[Note: I changed your word "number" to "rank" because "Jack", Queen",
and "King" are NOT numbers. "Ace" may be taken as "1" but those can't. lol]
For each of these 13 ways to choose the rank of the four cards,
there are 48 other cards we can choose for that odd fifth card.
So the answer is 13×48 or 624 ways.
Edwin