Multiply $ \color{blue}{6x} $ by $ \left( x+5\right) $ $$ \color{blue}{6x} \cdot \left( x+5\right) = 6x^2+30x $$

Multiply $ \color{blue}{x} $ by $ \left( x+6\right) $ $$ \color{blue}{x} \cdot \left( x+6\right) = x^2+6x $$

Remove the parentheses by changing the sign of each term within them.

$$ - \left( x^2+6x \right) = -x^2-6x $$

Multiply $6x^2+30x$ by $ \dfrac{x-5}{5-x^2-6x} $ to get $ \dfrac{6x^3-150x}{-x^2-6x+5} $.

Step 1: Write $ 6x^2+30x $ as a fraction by putting $ \color{red}{1} $ in the denominator.

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} 6x^2+30x \cdot \frac{x-5}{5-x^2-6x} & \xlongequal{\text{Step 1}} \frac{6x^2+30x}{\color{red}{1}} \cdot \frac{x-5}{5-x^2-6x} \xlongequal{\text{Step 2}} \frac{ \left( 6x^2+30x \right) \cdot \left( x-5 \right) }{ 1 \cdot \left( 5-x^2-6x \right) } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 6x^3 -\cancel{30x^2}+ \cancel{30x^2}-150x }{ 5-x^2-6x } = \frac{6x^3-150x}{-x^2-6x+5} \end{aligned} $$