1. The problem is to solve the expression $-8 + 13$. 2. This is a simple addition problem involving integers. 3. When adding a negative number and a positive number, subtract the smaller absolute value from the larger absolute value and take the sign of the number with the larger absolute value. 4. Calculate the absolute values: $|-8| = 8$ and $|13| = 13$. 5. Since $13 > 8$, subtract $8$ from $13$: $$13 - 8 = 5$$ 6. The sign of the result is positive because $13$ is positive. 7. Therefore, the final answer is $5$.