Subtract $ \dfrac{1}{3x} $ from $ \dfrac{1}{5x^3} $ to get $ \dfrac{ \color{purple}{ -5x^3+3x } }{ 15x^4 }$.

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}{ 3x }$ and the second by $\color{blue}{ 5x^3 }$.

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