The sample space is the set of all possible hands of five cards;

n(S) = 2,598,960.

The event E is the set of all possible hands of five cards excluding the hands of five red cards;

n(E) = 2,598,96065,780 = 2,533,180.

Therefore,

P(E)

=

n(E) n(S)

=

2,533,180 2,598,960

0.9747.