Add $ \dfrac{-5}{9} $ and $ \dfrac{5}{4x} $ to get $ \dfrac{ \color{purple}{ -20x+45 } }{ 36x }$.

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}{ 4x }$ and the second by $\color{blue}{ 9 }$.

$$ \begin{aligned} \frac{-5}{9} + \frac{5}{4x} & = \frac{ \left( -5 \right) \cdot \color{blue}{ 4x }}{ 9 \cdot \color{blue}{ 4x }} + \frac{ 5 \cdot \color{blue}{ 9 }}{ 4x \cdot \color{blue}{ 9 }} = \\[1ex] &=\frac{ \color{purple}{ -20x } }{ 36x } + \frac{ \color{purple}{ 45 } }{ 36x }=\frac{ \color{purple}{ -20x+45 } }{ 36x } \end{aligned} $$