Multiply $7$ by $ \dfrac{r}{4} $ to get $ \dfrac{ 7r }{ 4 } $.

Step 1: Write $ 7 $ as a fraction by putting $ \color{red}{1} $ in the denominator.

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} 7 \cdot \frac{r}{4} & \xlongequal{\text{Step 1}} \frac{7}{\color{red}{1}} \cdot \frac{r}{4} \xlongequal{\text{Step 2}} \frac{ 7 \cdot r }{ 1 \cdot 4 } \xlongequal{\text{Step 3}} \frac{ 7r }{ 4 } \end{aligned} $$

Add $ \dfrac{5}{r^5} $ and $ \dfrac{7r}{4} $ to get $ \dfrac{ \color{purple}{ 7r^6+20 } }{ 4r^5 }$.

To add raitonal expressions, both fractions must have the same denominator.
We can create a common denominator by multiplying the first fraction by $ \color{blue}{ 4 }$ and the second by $\color{blue}{ r^5 }$.

$$ \begin{aligned} \frac{5}{r^5} + \frac{7r}{4} & = \frac{ 5 \cdot \color{blue}{ 4 }}{ r^5 \cdot \color{blue}{ 4 }} + \frac{ 7r \cdot \color{blue}{ r^5 }}{ 4 \cdot \color{blue}{ r^5 }} = \\[1ex] &=\frac{ \color{purple}{ 20 } }{ 4r^5 } + \frac{ \color{purple}{ 7r^6 } }{ 4r^5 }=\frac{ \color{purple}{ 7r^6+20 } }{ 4r^5 } \end{aligned} $$