For a prime $p$ let $S(p)=(\sum (p-k)!)mod(p)$ for $1\le k\le 5$.

For example, if $p=7$,
$(7-1)!+(7-2)!+(7-3)!+(7-4)!+(7-5)!=6!+5!+4!+3!+2!=720+120+24+6+2=872$.
As $872mod(7)=4$, $S(7)=4$.

It can be verified that $\sum S(p)=480$ for $5\le p<100$.

Find $\sum S(p)$ for $5\le p<{10}^8$.