Yes. If we consider genealogical rather than genetic inheritance, then incredibly you only have to go back 5,000 years or so to find a common ancestor.
To me it's not even that incredible, after some thinking. The number of descendants (and ascendants) of a single person grows exponentially with time. Assuming that a certain closed population remains constant, it means that most of the 2^n descendants of a single person after n generations are actually a much smaller group of people counted many times each (i.e., through different lineages), for n large enough (but not even too much). So there is some "pressure" for essentially everybody in the closed population to eventually become descendant of a given person after a number of generations roughly comparable to the logarithm of the population size. Estimating that a generation take 25 years, 5000 years means 200 generations. 1.12^200 ~= 7 billion, so a logarithm base of 1.12 is already around enough to justify the common ancestor age.
The world population is not constant, of course, and it doesn't behave according to the assumptions I made implicitly, but the order of magnitude makes sense. A single person moving from a people to another is enough to unify the two lineages.
The world population is not constant, of course, and it doesn't behave according to the assumptions I made implicitly, but the order of magnitude makes sense. A single person moving from a people to another is enough to unify the two lineages.