The question asks about the number of ways to distribute 6 distinct balls into 5 distinct boxes. Let`s examine each option:

Option 1: 7776

This option suggests that there are 7776 ways to distribute the balls into the boxes. Since we have 6 balls and 5 boxes, this option implies that each ball has 6 choices of boxes to go into. However, this is incorrect because there are only 5 boxes available.

Option 2: 15625

This option states that there are 15625 ways to distribute the balls into the boxes. It correctly considers that each ball has 5 choices of boxes to go into. To determine if this option is correct, we can calculate the total number of possible distributions by taking the product of the number of choices for each ball, which is 5*5*5*5*5*5 = 15625. Therefore, this option is correct.

Option 3: 720

This option suggests that there are 720 ways to distribute the balls into the boxes. It could be a possible answer if there were fewer balls or boxes. However, since there are 6 balls and 5 boxes, it is not possible to have only 720 distributions. Hence, option