Multiply $c^5$ by $ \dfrac{d}{4} $ to get $ \dfrac{ c^5d }{ 4 } $.

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

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} c^5 \cdot \frac{d}{4} & \xlongequal{\text{Step 1}} \frac{c^5}{\color{red}{1}} \cdot \frac{d}{4} \xlongequal{\text{Step 2}} \frac{ c^5 \cdot d }{ 1 \cdot 4 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ c^5d }{ 4 } \end{aligned} $$

Add $ \dfrac{c^5d}{4} $ and $ \dfrac{1}{4} $ to get $ \dfrac{ c^5d + 1 }{ \color{blue}{ 4 }}$.

To add expressions with the same denominators, we add the numerators and write the result over the common denominator.

$$ \begin{aligned} \frac{c^5d}{4} + \frac{1}{4} & = \frac{c^5d}{\color{blue}{4}} + \frac{1}{\color{blue}{4}} =\frac{ c^5d + 1 }{ \color{blue}{ 4 }} \end{aligned} $$