Subtract $7c+8$ from $ \dfrac{b^4}{5} $ to get $ \dfrac{ \color{purple}{ b^4-35c-40 } }{ 5 }$.

Step 1: Write $ 7c+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 $\color{blue}{5}$.

$$ \begin{aligned} \frac{b^4}{5} -7c+8 & \xlongequal{\text{Step 1}} \frac{b^4}{5} - \frac{7c+8}{\color{red}{1}} = \frac{ b^4 }{ 5 } - \frac{ \left( 7c+8 \right) \cdot \color{blue}{ 5 }}{ 1 \cdot \color{blue}{ 5 }} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ b^4 } }{ 5 } - \frac{ \color{purple}{ 35c+40 } }{ 5 }=\frac{ \color{purple}{ b^4 - \left( 35c+40 \right) } }{ 5 } = \\[1ex] &=\frac{ \color{purple}{ b^4-35c-40 } }{ 5 } \end{aligned} $$