About DNA tests

Is there a genetic test that displays your complete ancestry (i.e. going back more than 5 generations)? I am curious to see if my great-great grandmother (on my mother's side) had any close Semitic ancestry - I would be very surprised if she didn't - so I was wondering if there is a suitable test for this. I am very ignorant on these matters.

In essence, what is the most comprehensive DNA test that I can order?

Then you better should analyze the DNA from your mother or your great-mother.