Subtract $ \dfrac{4}{7} $ from $ \dfrac{5}{3} $ to get $ \dfrac{ \color{purple}{ 23 } }{ 21 }$.

To subtract fractions they must have the same denominator.
We can create a common denominator by multiplying the first fraction by $ \color{blue}{ 7 }$ and the second by $\color{blue}{ 3 }$.

$$ \begin{aligned} \frac{5}{3} - \frac{4}{7} & = \frac{ 5 \cdot \color{blue}{ 7 }}{ 3 \cdot \color{blue}{ 7 }} - \frac{ 4 \cdot \color{blue}{ 3 }}{ 7 \cdot \color{blue}{ 3 }} = \\[1ex] &=\frac{ \color{purple}{ 35 } }{ 21 } - \frac{ \color{purple}{ 12 } }{ 21 }=\frac{ \color{purple}{ 23 } }{ 21 } \end{aligned} $$