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?