Subtract $ \dfrac{4}{5} $ from $ \dfrac{a}{3} $ to get $ \dfrac{ \color{purple}{ 5a-12 } }{ 15 }$.

To subtract raitonal expressions, both fractions must have the same denominator.
We can create a common denominator by multiplying the first fraction by $ \color{blue}{ 5 }$ and the second by $\color{blue}{ 3 }$.

$$ \begin{aligned} \frac{a}{3} - \frac{4}{5} & = \frac{ a \cdot \color{blue}{ 5 }}{ 3 \cdot \color{blue}{ 5 }} - \frac{ 4 \cdot \color{blue}{ 3 }}{ 5 \cdot \color{blue}{ 3 }} = \\[1ex] &=\frac{ \color{purple}{ 5a } }{ 15 } - \frac{ \color{purple}{ 12 } }{ 15 }=\frac{ \color{purple}{ 5a-12 } }{ 15 } \end{aligned} $$