Certainly Chinese history in terms of a continuous lineage of culture surpasses even that of the Egyptians (they don't exactly write in hieroglyphics nowadays), but '5,000 years' is a little of an overstatement, nonetheless.

The earliest evidence of writing, for example, is about 3,500 years ago, and before that, the Xia dynasty was little more than legend. Scholars found that the stories about the Xia was the total opposite of the Shang (the first dynasty with evidence), which comes across more like folktale propaganda, making the past look bad sorta thing.

Recently they discovered what appears to be like, a hut by a river where the Xia dynasty was said to be, and evidence of the fabled flood, though the dates of these were closer to 3900 years ago.

It may be picky to knock off merely 1,000 years but that's the equivalent of all modern history in the west pretty much.

Aside from that, given that there was no written document and only fables from those times, and perhaps a small village at best, it's no different from any other of the numerous civilisations that had been around at least 10,000 years ago such as in Turkey. China can join the dots based on proximity alone if they want, but I can do that with Cheddar man, found in the UK from 9,000 years ago. It's a little disingenuous.

Realistically, they have about 3,500 years of solid history, I'd say. Which is still impressive.