what is the probability of a six card hand cantoning no fives?

Answer 1

probability of one 5 = 4/52
probability of two 5s = 4/52*3/51
probability of three 5s =4/52*3/51*2/50
probability of four 5s=4/52*3/51*2/50*1/49
so probability of at least one 5 = sum of all those
subtract that from 1 to get the probability of none.

Answer 2

or
number of six card hands = C(52,6)
number of six card hands with no fives = C(48,6)

prob of your event = C(48,6)/C(52,6) = .60277