Subtract $ \dfrac{z^2}{4} $ from $ y+5 $ to get $ \dfrac{ \color{purple}{ -z^2+4y+20 } }{ 4 }$.

Step 1: Write $ y+5 $ 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 $\color{blue}{ 4 }$.

$$ \begin{aligned} y+5- \frac{z^2}{4} & \xlongequal{\text{Step 1}} \frac{y+5}{\color{red}{1}} - \frac{z^2}{4} = \frac{ \left( y+5 \right) \cdot \color{blue}{ 4 }}{ 1 \cdot \color{blue}{ 4 }} - \frac{ z^2 }{ 4 } = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ 4y+20 } }{ 4 } - \frac{ \color{purple}{ z^2 } }{ 4 }=\frac{ \color{purple}{ -z^2+4y+20 } }{ 4 } \end{aligned} $$