Add $ \dfrac{1}{5} $ and $ \dfrac{2}{3} $ to get $ \dfrac{ \color{purple}{ 13 } }{ 15 }$.

To add fractions they must have the same denominator.
We can create a common denominator by multiplying the first fraction by $ \color{blue}{ 3 }$ and the second by $\color{blue}{ 5 }$.

$$ \begin{aligned} \frac{1}{5} + \frac{2}{3} & = \frac{ 1 \cdot \color{blue}{ 3 }}{ 5 \cdot \color{blue}{ 3 }} + \frac{ 2 \cdot \color{blue}{ 5 }}{ 3 \cdot \color{blue}{ 5 }} = \\[1ex] &=\frac{ \color{purple}{ 3 } }{ 15 } + \frac{ \color{purple}{ 10 } }{ 15 }=\frac{ \color{purple}{ 13 } }{ 15 } \end{aligned} $$