Answer
diverges
Work Step by Step
Let us suppose that the function $f(x)=\dfrac{x^3}{5x^4+3}$
This implies that $f'(x)=\dfrac{9x^2-5x^6}{(5x^4+3)^2}$
Next, $\lim\limits_{n \to \infty} n a_n=n \times \lim\limits_{n \to \infty} \dfrac{n^3}{5n^4+3}=\dfrac{1}{5}$
and $\dfrac{1}{5} \gt 0$
This means that the given series has a finite value, so it is diverges.
