Solve for x

$\displaystyle 1!+2!+\dots +1000! \equiv x \ \mbox{(mod 10)}$

The book say when $\displaystyle k\geq 5, k!\equiv 0 \ \mbox{(mod 10)} \ \mbox{and} \ \mbox{(mod 15)}$.

Why is this? And how am I supposed to use this to solve this problem?