Combine like terms:

$$ 5+ \color{blue}{i} + \color{blue}{2i} = \color{blue}{3i} +5 $$

Add $3i+5$ and $ \dfrac{5}{2} $ to get $ \dfrac{ \color{purple}{ 6i+15 } }{ 2 }$.

Step 1: Write $ 3i+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 $\color{blue}{ 2 }$.

$$ \begin{aligned} 3i+5+ \frac{5}{2} & \xlongequal{\text{Step 1}} \frac{3i+5}{\color{red}{1}} + \frac{5}{2} = \frac{ \left( 3i+5 \right) \cdot \color{blue}{ 2 }}{ 1 \cdot \color{blue}{ 2 }} + \frac{ 5 }{ 2 } = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ 6i+10 } }{ 2 } + \frac{ \color{purple}{ 5 } }{ 2 }=\frac{ \color{purple}{ 6i+15 } }{ 2 } \end{aligned} $$