$$ i^3 = \color{blue}{i^2} \cdot i = ( \color{blue}{-1}) \cdot i = - \, i $$$$ i^{18} = i^{4 \cdot 4 + 2} = \left( i^4 \right)^{ 4 } \cdot i^2 = 1^{ 4 } \cdot (-1) = -1 = -1 $$

Add $ \dfrac{5}{i} $ and $ \dfrac{2}{-i} $ to get $ \dfrac{ \color{purple}{ -3i } }{ -i^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}{ -i }$ and the second by $\color{blue}{ i }$.

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

Place minus sign in front of the fraction.

$$ -i^2 = -(-1) = 1 $$

Remove 1 from denominator.

Subtract $-20$ from $ \dfrac{-3i}{1} $ to get $ \dfrac{ -3i - \left( -20 \right) }{ \color{blue}{ 1 }}$.

Step 1: Write $ -20 $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator.

Step 2: To subtract expressions with the same denominators, we subtract the numerators and write the result over the common denominator.

$$ \begin{aligned} \frac{-3i}{1} --20 & \xlongequal{\text{Step 1}} \frac{-3i}{1} - \frac{-20}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{-3i}{\color{blue}{1}} - \frac{-20}{\color{blue}{1}} = \\[1ex] &=\frac{ -3i - \left( -20 \right) }{ \color{blue}{ 1 }} \end{aligned} $$