"Actually the low end of carbon 14 dating is on the order of 50,000 years."
No. 5,000 years is as accurate as it can get because we have enough knowledge to make the necessary adjustments. Since we lack knowledge beyond that - climate etc. it's guesswork.
Well you are wrong. Carbon dating is routinely used throughout archealogy, paleontology, and other sciences for dating far beyond 5,000 years. We have plenty of other callibration tools such as tree rings and ice cores that continually provide confirmation of the accuracy of carbon dating.