Sorry Gaile but that's not true (that autosomal DNA isn't going further than 4 generations).
I can already see the damage done with this wrong statement as it's selected as the best answer in another question.
I have referenced to the work of Professor Itsik Pe'er in several G2G answers already (I wish I could easily reference it but I'm not able to search for it).
IBD segments go way beyond 4 generations and depending on the threshold you're applying (most DNA testing companies use 7 cM) you're going back to different time periods where the common ancestor is from.
I strongly suggest you watch Professor Pe'er's talk: Identity by descent in medical and ancient population genomics - if you eg. just go to 15:38 of his presentation you see a slide where Professor Pe'er shows that IBD segments between 0.5 to 10 cM do come from a common ancestor between 5 and 99 generations back.
Later on in the video he's also presenting his work on the "The Genome of Netherlands" project which shows estimates of the period where the common ancestor has lived for 1 cM brackets start from 1-2 cM (up to 2200 BCE) to > 7 cM (1500 CE onwards).
So in conclusion there is a possibility to identify common ancestors that far back however this would involve a large number of descendants of this common ancestor and looking at each potential permutation (comparison) between all people who are in such a triangulated group with a direct line to the common ancestor.
As there are for sure several possible lines between the common ancestor and the DNA tested people (meaning you're a descendant in more than one way) it can be assumed that there will be several different triangulated groups, not just one.