Multiply $5$ by $ \dfrac{x}{4} $ to get $ \dfrac{ 5x }{ 4 } $.

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

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} 5 \cdot \frac{x}{4} & \xlongequal{\text{Step 1}} \frac{5}{\color{red}{1}} \cdot \frac{x}{4} \xlongequal{\text{Step 2}} \frac{ 5 \cdot x }{ 1 \cdot 4 } \xlongequal{\text{Step 3}} \frac{ 5x }{ 4 } \end{aligned} $$

Add $ \dfrac{5x}{4} $ and $ \dfrac{x}{6} $ to get $ \dfrac{ \color{purple}{ 17x } }{ 12 }$.

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}{ 3 }$ and the second by $\color{blue}{ 2 }$.

$$ \begin{aligned} \frac{5x}{4} + \frac{x}{6} & = \frac{ 5x \cdot \color{blue}{ 3 }}{ 4 \cdot \color{blue}{ 3 }} + \frac{ x \cdot \color{blue}{ 2 }}{ 6 \cdot \color{blue}{ 2 }} = \\[1ex] &=\frac{ \color{purple}{ 15x } }{ 12 } + \frac{ \color{purple}{ 2x } }{ 12 }=\frac{ \color{purple}{ 17x } }{ 12 } \end{aligned} $$