Yahtzee is a family game played with five normal six-sided dice. In each turn, a player rolls the five dice and can keep some of the numbers and roll the remaining dice. After the second roll, the player can choose to keep more numbers and roll the remaining dice a final time. At the end of a Yahtzee game recently, Smith needed to roll at least one 5 to get a 35-point bonus and win the game. He rolled all five dice once, twice, and then a third time and did not get any 5s. What are the chances of this happening?