To add or subtract expressions, expand them to make their denominators the same. Least common multiple of $5\left(x-5\right)$ and $6\left(-x+5\right)$ is $30\left(x-5\right)$. Multiply $\frac{8}{5\left(x-5\right)}$ times $\frac{6}{6}$. Multiply $\frac{6}{6\left(-x+5\right)}$ times $\frac{-5}{-5}$.
Since $\frac{8\times 6}{30\left(x-5\right)}$ and $\frac{6\left(-5\right)}{30\left(x-5\right)}$ have the same denominator, subtract them by subtracting their numerators.
