Non-Elementary Integration · Easy problem

The Gamma function satisfies $\Gamma(s+1)=s\,\Gamma(s)$. Without evaluating either integral, find $\dfrac{\Gamma(6)}{\Gamma(4)}=\dfrac{\displaystyle\int_0^{\infty}x^{5}e^{-x}\,dx}{\displaystyle\int_0^{\infty}x^{3}e^{-x}\,dx}$.