Find all natural numbers $n$ such that $7n^3 < 5^n$.

I drew a graph which showed that $n \geq 4$

[wolfram](http://www.wolframalpha.com/input/?i=7n%5E3+%3C+5%5En)

How can I prove that? I guess I need to use induction with the base case $n=4$?

But I am stuck because the induction hypothesis uses a $\geq$ sign so I can not substitute...