Subtract $6$ from $ \dfrac{w}{w+5} $ to get $ \dfrac{ \color{purple}{ -5w-30 } }{ w+5 }$.

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

Step 2: To subtract raitonal expressions, both fractions must have the same denominator.
We can create a common denominator by multiplying the second fraction by $\color{blue}{w+5}$.

$$ \begin{aligned} \frac{w}{w+5} -6 & \xlongequal{\text{Step 1}} \frac{w}{w+5} - \frac{6}{\color{red}{1}} = \frac{ w }{ w+5 } - \frac{ 6 \cdot \color{blue}{ \left( w+5 \right) }}{ 1 \cdot \color{blue}{ \left( w+5 \right) }} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ w } }{ w+5 } - \frac{ \color{purple}{ 6w+30 } }{ w+5 }=\frac{ \color{purple}{ w - \left( 6w+30 \right) } }{ w+5 } = \\[1ex] &=\frac{ \color{purple}{ -5w-30 } }{ w+5 } \end{aligned} $$