The problem requires determining the new average when each number of a set is divided by 3, given that the original average is 15.

1. The average of a set of numbers is calculated as the sum of the numbers divided by the total count of numbers. 
   Let us denote the sum of the original five numbers as \(S\). Given that the average is 15, we have: \(\frac{S}{5} = 15\).
2. From the equation in step 1, we can find \(S\):

\(S = 15 \times 5 = 75\)

1. When each number is divided by 3, the sum of the new numbers becomes \(\frac{S}{3}\). 
   Thus, the sum of the numbers becomes:

\(\frac{75}{3} = 25\)

1. Now, calculate the average of the new set of numbers. Since the total count remains the same (five numbers), the new average will be:

\(\frac{25}{5} = 5\)

Thus, the average of the new set of numbers when each number is divided by 3 becomes 5.

The correct answer is 5, which matches the provided correct answer.