Here's the way I see this........
If the number is a multiple of 5, it must end in a "5"......and there are 5! = 120 ways of arranging the other digits
Of the numbers of interest.....the "6" has to be the first digit if the number is > 500,000 and the "5" has to be the last
Thus....the "middle digits" in these numbers can be arranged in 4! = 24 ways
So...the probability is 24 / 120 = 1 / 5
Edited to correct an earlier answer......
Actually the right answer is 1/6 because there is only one digit that works, and that is the 6. Therefore the probability is 1/6. Technically, you could generate all those outcomes for each digit. I believe that the correct answer is 1/6.
The generated numbers are constrained to multiples of five, so (5) has to be used in the units position. This leaves five (5) numbers [1,2,3,4,6] to choose for the first digit, and six (6) is the only number that produces numbers greater than 500,000. (The arrangement of the remaining numbers are irrelevant.)
The probability is 1/5