Add $5$ and $ \dfrac{24}{j+7} $ to get $ \dfrac{ \color{purple}{ 5j+59 } }{ j+7 }$.

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

Step 2: To add raitonal expressions, both fractions must have the same denominator.
We can create a common denominator by multiplying the first fraction by $\color{blue}{ j+7 }$.

$$ \begin{aligned} 5+ \frac{24}{j+7} & \xlongequal{\text{Step 1}} \frac{5}{\color{red}{1}} + \frac{24}{j+7} = \frac{ 5 \cdot \color{blue}{ \left( j+7 \right) }}{ 1 \cdot \color{blue}{ \left( j+7 \right) }} + \frac{ 24 }{ j+7 } = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ 5j+35 } }{ j+7 } + \frac{ \color{purple}{ 24 } }{ j+7 }=\frac{ \color{purple}{ 5j+59 } }{ j+7 } \end{aligned} $$