Testing atDNA can reveal background ethnicity to the 10th generation, but if you're trying to establish a relationship between particular individuals, past the level of a 5th cousin you're on shaky ground unless you have additional, strongly supportive data. From
https://isogg.org/wiki/Autosomal_DNA :
"Autosomal DNA tests can be used to confirm relationships with a high level of accuracy for parent/child relationships and all relationships up to the second cousin level. For all relationships additional contextual and genealogical information is required to confirm the nature of the relationship.... Genealogical relationships beyond the 5th cousin level of relationship are more difficult to prove with autosomal DNA testing and, as a general rule, these can only be approached using triangulation."
If some way could be found to accurately interpret data revealing shared atDNA past the level of 5th cousins, that would be a remarkable advance, but the quantity of shared DNA past that level is so small that it's not now possible to rely on test results for anything beyond speculative conclusions.
