Show using the monotonic convergence theorem that the limit below convergence, in other words, analytically demonstrate that the limit below convergence:

$$ lim_ {x to infty} frac {5 ^ x} {2 ^ {n ^ 2}} $$

I tried to do: $$ lim_ {x to infty} frac {x cdot ln {5}} {x ^ 2 cdot ln {2}} = 0 $$ but I do not know if this is allowed by the theorem.