Subtract $ \dfrac{40}{m} $ from $ 5m $ to get $ \dfrac{ \color{purple}{ 5m^2-40 } }{ m }$.

Step 1: Write $ 5m $ 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 first fraction by $\color{blue}{ m }$.

$$ \begin{aligned} 5m- \frac{40}{m} & \xlongequal{\text{Step 1}} \frac{5m}{\color{red}{1}} - \frac{40}{m} = \frac{ 5m \cdot \color{blue}{ m }}{ 1 \cdot \color{blue}{ m }} - \frac{ 40 }{ m } = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ 5m^2 } }{ m } - \frac{ \color{purple}{ 40 } }{ m }=\frac{ \color{purple}{ 5m^2-40 } }{ m } \end{aligned} $$

Subtract $8$ from $ \dfrac{5m^2-40}{m} $ to get $ \dfrac{ \color{purple}{ 5m^2-8m-40 } }{ m }$.

Step 1: Write $ 8 $ 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 $\color{blue}{m}$.

$$ \begin{aligned} \frac{5m^2-40}{m} -8 & \xlongequal{\text{Step 1}} \frac{5m^2-40}{m} - \frac{8}{\color{red}{1}} = \frac{ 5m^2-40 }{ m } - \frac{ 8 \cdot \color{blue}{ m }}{ 1 \cdot \color{blue}{ m }} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ 5m^2-40 } }{ m } - \frac{ \color{purple}{ 8m } }{ m }=\frac{ \color{purple}{ 5m^2-8m-40 } }{ m } \end{aligned} $$