Multiply $ \dfrac{25}{6} $ by $ b $ to get $ \dfrac{ 25b }{ 6 } $.

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

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} \frac{25}{6} \cdot b & \xlongequal{\text{Step 1}} \frac{25}{6} \cdot \frac{b}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 25 \cdot b }{ 6 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 25b }{ 6 } \end{aligned} $$

Add $36b^2+60b$ and $ \dfrac{25b}{6} $ to get $ \dfrac{ \color{purple}{ 216b^2+385b } }{ 6 }$.

Step 1: Write $ 36b^2+60b $ 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 $\color{blue}{ 6 }$.

$$ \begin{aligned} 36b^2+60b+ \frac{25b}{6} & \xlongequal{\text{Step 1}} \frac{36b^2+60b}{\color{red}{1}} + \frac{25b}{6} = \frac{ \left( 36b^2+60b \right) \cdot \color{blue}{ 6 }}{ 1 \cdot \color{blue}{ 6 }} + \frac{ 25b }{ 6 } = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ 216b^2+360b } }{ 6 } + \frac{ \color{purple}{ 25b } }{ 6 }=\frac{ \color{purple}{ 216b^2+385b } }{ 6 } \end{aligned} $$

Add $ \dfrac{216b^2+385b}{6} $ and $ 5 $ to get $ \dfrac{ \color{purple}{ 216b^2+385b+30 } }{ 6 }$.

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 second fraction by $\color{blue}{6}$.

$$ \begin{aligned} \frac{216b^2+385b}{6} +5 & \xlongequal{\text{Step 1}} \frac{216b^2+385b}{6} + \frac{5}{\color{red}{1}} = \frac{ 216b^2+385b }{ 6 } + \frac{ 5 \cdot \color{blue}{ 6 }}{ 1 \cdot \color{blue}{ 6 }} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ 216b^2+385b } }{ 6 } + \frac{ \color{purple}{ 30 } }{ 6 }=\frac{ \color{purple}{ 216b^2+385b+30 } }{ 6 } \end{aligned} $$