Multiply $5$ by $ \dfrac{x^3}{10} $ to get $ \dfrac{ 5x^3 }{ 10 } $.

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.

$$ \begin{aligned} 5 \cdot \frac{x^3}{10} & \xlongequal{\text{Step 1}} \frac{5}{\color{red}{1}} \cdot \frac{x^3}{10} \xlongequal{\text{Step 2}} \frac{ 5 \cdot x^3 }{ 1 \cdot 10 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 5x^3 }{ 10 } \end{aligned} $$

Multiply $ \dfrac{5x^3}{10} $ by $ x^2 $ to get $ \dfrac{ 5x^5 }{ 10 } $.

Step 1: Write $ x^2 $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator.

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} \frac{5x^3}{10} \cdot x^2 & \xlongequal{\text{Step 1}} \frac{5x^3}{10} \cdot \frac{x^2}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 5x^3 \cdot x^2 }{ 10 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 5x^5 }{ 10 } \end{aligned} $$

Add $ \dfrac{5x^5}{10} $ and $ 5x $ to get $ \dfrac{ \color{purple}{ 5x^5+50x } }{ 10 }$.

Step 1: Write $ 5x $ 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 second fraction by $\color{blue}{10}$.

$$ \begin{aligned} \frac{5x^5}{10} +5x & \xlongequal{\text{Step 1}} \frac{5x^5}{10} + \frac{5x}{\color{red}{1}} = \frac{ 5x^5 }{ 10 } + \frac{ 5x \cdot \color{blue}{ 10 }}{ 1 \cdot \color{blue}{ 10 }} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ 5x^5 } }{ 10 } + \frac{ \color{purple}{ 50x } }{ 10 }=\frac{ \color{purple}{ 5x^5+50x } }{ 10 } \end{aligned} $$