Add $-2$ and $ \dfrac{i}{5} $ to get $ \dfrac{ \color{purple}{ i-10 } }{ 5 }$.

Step 1: Write $ -2 $ 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 $\color{blue}{ 5 }$.

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

Subtract $ \dfrac{10+2i}{5} $ from $ \dfrac{-i+10}{5} $ to get $ \dfrac{-3i}{5} $.

To subtract expressions with the same denominators, we subtract the numerators and write the result over the common denominator.

$$ \begin{aligned} \frac{-i+10}{5} - \frac{10+2i}{5} & = \frac{-i+10}{\color{blue}{5}} - \frac{10+2i}{\color{blue}{5}} =\frac{ -i+10 - \left( 10+2i \right) }{ \color{blue}{ 5 }} = \\[1ex] &= \frac{-3i}{5} \end{aligned} $$