discrete mathematics - Proof by Induction: $n! > 2^{n+1}$ for all integers $n geq 5.$

I have to answer this question for my math class and am having a little trouble with it.

Use mathematical induction to prove that $n! > 2^{n+1}$ for all integers $n \geq 5.$

For the basis step: $(n = 5)$

$5! = 120$

$2^{5+1} = 2^6 = 64$

So $120 > 64$, which is true.

For the induction step, this is as far as I've gotten:

Prove that $(n! > 2^{n+1}) \rightarrow \left((n+1)! > 2^{(n+1)+1}\right)$

Assume $n! > 2^{(n+1)}$
Then $(n+1)! = (n+1) \cdot n!$

After this, I'm stuck. Any assistance would be appreciated.

Thanks!