Factorial Greater than Cube for n Greater than 5/Proof 2

Proof
For $n > 5$, notice that the following inequalities hold:


 * $2 \paren {n - 1} = 2 n - 2 > n + 5 - 2 > n$


 * $3 \paren {n - 2} = 3 n - 6 > n + 10 - 6 > n$

And thus: