There are 50 integers to choose from between 20 and 69, inclusive. To have a different tens digit, the integers must be chosen from the set {20, 21, 22, ... , 29, 30, 31, ... , 69}. We can select the first integer in 50 ways. The second integer must be chosen from 49 remaining integers, the third integer from 48 remaining integers and so on.
So the probability of selecting 5 different integers with different tens digit is (50*49*48*47*46)/(50^5) = 317814/390625.
