Subtract $3i$ from $ \dfrac{5+2r}{5} $ to get $ \dfrac{ \color{purple}{ -15i+2r+5 } }{ 5 }$.

Step 1: Write $ 3i $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator.

Step 2: To subtract raitonal expressions, both fractions must have the same denominator.
We can create a common denominator by multiplying the second fraction by $\color{blue}{5}$.

$$ \begin{aligned} \frac{5+2r}{5} -3i & \xlongequal{\text{Step 1}} \frac{5+2r}{5} - \frac{3i}{\color{red}{1}} = \frac{ 5+2r }{ 5 } - \frac{ 3i \cdot \color{blue}{ 5 }}{ 1 \cdot \color{blue}{ 5 }} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ 5+2r } }{ 5 } - \frac{ \color{purple}{ 15i } }{ 5 }=\frac{ \color{purple}{ -15i+2r+5 } }{ 5 } \end{aligned} $$