Add $ \dfrac{5}{a} $ and $ \dfrac{6}{b} $ to get $ \dfrac{ \color{purple}{ 6a+5b } }{ ab }$.

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

$$ \begin{aligned} \frac{5}{a} + \frac{6}{b} & = \frac{ 5 \cdot \color{blue}{ b }}{ a \cdot \color{blue}{ b }} + \frac{ 6 \cdot \color{blue}{ a }}{ b \cdot \color{blue}{ a }} = \\[1ex] &=\frac{ \color{purple}{ 5b } }{ ab } + \frac{ \color{purple}{ 6a } }{ ab }=\frac{ \color{purple}{ 6a+5b } }{ ab } \end{aligned} $$