Below is my solution. Is this sufficient enough to prove?
$$|x^3+5x| \le |x^3+5x^3|$$
$$x^3 + 5^x \le 6x^3, x > 1, C=6$$
Let's take $x = 2$.
$$f(x) = (2)^3 + 5(2) = 18$$
$$g(x) = 6\cdot 8 = 48$$
For when $x > 1 |f(x)| \le C|g(x)|$ is false hence proving $x^3 + 5x$ is not $O(x^2)$.
