Explanation:

- To solve this problem, we first find the work rate of girls and boys.

- Let the work done by 1 girl in 1 day be $g$, and by 1 boy be $b$.

- Equation from the first scenario: $8g+12b=\frac{1}{4}$.

- Equation from the second scenario: $10g+6b=\frac{1}{6}$.

- Solve these equations simultaneously to find values of $g$ and $b$.

- Calculate the combined work rate of 5 girls and 3 boys: $5g+3b$.

- Find the total time taken for 5 girls and 3 boys to complete the work.

- After calculation, it is found that 5 girls and 3 boys will take 13 days.

- Therefore, Option: 4 (13 days) is correct.

Option: 4 - 13 days is the correct answer.