elementary number theory - Finding the remainder of a factorial using modular arithmetic

How do I find the remainder of $5^{2001} + (27)!$ when it is divided by $8$? Can someone please show me the appropriate steps? I'm having a hard time with modular arithmetic.

So far this is how far I've got:

$$5^2=25 \equiv 1\pmod{8}$$

So $$\begin{align}5^{2001}&=5^{2000}\cdot 5\\ &=(5^2)^{1000}\cdot 5\\ &=25^{1000}\cdot 5\\ &\equiv 1^{1000}\cdot 5\\ &\equiv 5 \pmod{8}\end{align}$$

How do I go about somthing similar for $27!$? Also, could someone direct me to a video or some notes where I can learn this?