The fifth and eighth terms of a geometric sequence of real numbers are $7!$ and $8!$ respectively.  What is the first term?

$\mathrm{(A)}\ 60\qquad \mathrm{(B)}\ 75\qquad \mathrm{(C)}\ 120\qquad \mathrm{(D)}\ 225\qquad \mathrm{(E)}\ 315$
Let the $n$th term of the series be $ar^{n-1}$.  Because
\[\frac {8!}{7!} = \frac {ar^7}{ar^4} = r^3 = 8,\]
it follows that $r = 2$ and the first term is $a = \frac {7!}{r^4} = \frac {7!}{16} = \boxed{315}$.  The answer is $\mathrm{(E)}$.