Multiply $5$ by $ \dfrac{x}{5x+20} $ to get $ \dfrac{ 5x }{ 5x+20 } $.

Step 1: Write $ 5 $ as a fraction by putting $ \color{red}{1} $ in the denominator.

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} 5 \cdot \frac{x}{5x+20} & \xlongequal{\text{Step 1}} \frac{5}{\color{red}{1}} \cdot \frac{x}{5x+20} \xlongequal{\text{Step 2}} \frac{ 5 \cdot x }{ 1 \cdot \left( 5x+20 \right) } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 5x }{ 5x+20 } \end{aligned} $$

Subtract $ \dfrac{x}{2x+8} $ from $ \dfrac{5x}{5x+20} $ to get $ \dfrac{ \color{purple}{ 5x } }{ 10x+40 }$.

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

$$ \begin{aligned} \frac{5x}{5x+20} - \frac{x}{2x+8} & = \frac{ 5x \cdot \color{blue}{ 2 }}{ \left( 5x+20 \right) \cdot \color{blue}{ 2 }} - \frac{ x \cdot \color{blue}{ 5 }}{ \left( 2x+8 \right) \cdot \color{blue}{ 5 }} = \\[1ex] &=\frac{ \color{purple}{ 10x } }{ 10x+40 } - \frac{ \color{purple}{ 5x } }{ 10x+40 }=\frac{ \color{purple}{ 5x } }{ 10x+40 } \end{aligned} $$