In the game “Drop Dead,” you roll a number of six-sided dice. If a roll does not include any 2s or 5s, you add the sum of the dice to your score and roll all of the dice again.

If your roll does include 2s or 5s, you receive no points for that roll, the dice with 2s or 5s are discarded, and the remaining dice are rolled again. You repeat this procedure until all dice have been discarded.

If you start with five dice, what is your expected score by the time you have discarded all of your dice?