To solve the problem, we need to determine the probability that the sum of the numbers rolled on two dice is 5, given that the sum is odd.

Step 1: Total outcomes where the sum is odd

For two dice, the sum is odd when one die shows an odd number and the other shows an even number.

• The odd numbers on a die are: 1, 3, 5.
• The even numbers on a die are: 2, 4, 6.

For each combination, we can either have:

• The first die odd and the second die even.
• The first die even and the second die odd.

Each die has 3 possibilities for odd and 3 possibilities for even, leading to:

• $3 \times 3 = 9$ outcomes where the sum is odd for each of the two cases (odd-even or even-odd).

Thus, the total number of outcomes where the sum is odd is: [ 9 + 9 = 18