I will assume that there are 12 black cards and 12 red cards.
There are: . possible 5-card hands.There are 24 cards and you get 5 cards.
What is the probability of having more than 3 black cards
"More than 3 black cards" means "4 blacks cards or 5 black cards".
. . To get 4 black cards and 1 red, there are: . ways.
. . To get 5 black cards, there are: . ways.
Hence, there are: . ways to get more than 3 black cards.