Add $ \dfrac{2}{a} $ and $ \dfrac{3}{a-5} $ to get $ \dfrac{ \color{purple}{ 5a-10 } }{ a^2-5a }$.

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}{ a-5 }$ and the second by $\color{blue}{ a }$.

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