Why $(x-5)^2-4$ can be factorised as $(x-5-2)(x-5+2)$ I would like to understand why $(x-5)^2-4$ can be factorised as $(x-5-2)(x-5+2)$
I am particularly concerned with the term, $-4$.

It's Quite Simple.. 
You know, $a^2 - b^2 = (a-b)(a+b)$
Now, $(x-5)^2 - 4 = (x-5)^2-2^2$
Let $a=x-5 $ and $b=2$
So, $a^2-b^2 = (x-5)^2-2^2 = (a-b)(a+b)=(x-5-2)(x-5+2)$
