Do they take taxes out of Ga lottery on 5000 before you collect?

Assuming you are not a non-resident alien, there is no federal withholding on a prize of exactly $5000 unless you are subject to backup withholding. On a prize of $5000.01 or more, there would be withholding.

Georgia withholds at a rate of 6%. Several documents I found say this applies to prizes of "more than $5000." However, I looked up the actual Georgia code and it says "$5000 or more."

Whether they take any taxes out or not, you still have to declare the full amount on your tax return at the end of the year and pay taxes at that time.