Subtract $ \dfrac{5}{x} $ from $ \dfrac{3}{x-7} $ to get $ \dfrac{ \color{purple}{ -2x+35 } }{ x^2-7x }$.

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}{ x }$ and the second by $\color{blue}{ x-7 }$.

$$ \begin{aligned} \frac{3}{x-7} - \frac{5}{x} & = \frac{ 3 \cdot \color{blue}{ x }}{ \left( x-7 \right) \cdot \color{blue}{ x }} - \frac{ 5 \cdot \color{blue}{ \left( x-7 \right) }}{ x \cdot \color{blue}{ \left( x-7 \right) }} = \\[1ex] &=\frac{ \color{purple}{ 3x } }{ x^2-7x } - \frac{ \color{purple}{ 5x-35 } }{ x^2-7x }=\frac{ \color{purple}{ 3x - \left( 5x-35 \right) } }{ x^2-7x } = \\[1ex] &=\frac{ \color{purple}{ -2x+35 } }{ x^2-7x } \end{aligned} $$