prove limit by definition

Hello everyone, this is my first topic on this forum, so if by chance this question was asked in the past, redirect me to the relevant post.

So, I understand the definition of function limit, I just can't figure how to solve those problems.

For example, I have

$\displaystyle lim(x->2)(x²-4)=5$

So I write |x²-9|<ε, 0<|x-2|<δ

then

|x-3||x+3|<ε

and what's now? I know that probably I should assume that δ<1 or something, and then I stuck.

If there a place when I can see just a big amount of examples, this would be great.

Thank you.