#1 Find P(all five cards are different types)
#2 Find P(Straight | five different types)
#3 Find P(Flush | five different types)
#4 Find P(#2 and #3 both occur)
#5 Subtract (#2 + #3 - #4) from 1 (not #1)
#6 Multiply #1 times #5
I'm not going to solve the whole thing but these steps aren't too difficult individually.
