Even in Chinese schools we are told in history classes that we really don't have five thousands years of real history. It is just an often used, maybe canonized, phrase to emphasize our long history. I really would not get distracted over it.
Back to the 5K-year claim. It seems just rhetoric, but it actually enlarges unnecessary national pride, and then rhetoric becomes an unchallengeable truth. The "truth" then sounds so true that foreigners starts to believe it without hesitation.
Once I had a chat with an American friend, about Chinese character system and its ability to maintain information through the past five thousand years. I was astonished that nowadays some foreigners might still view East Asia as the mysterious Far East.
https://www.washingtonpost.com/news/speaking-of-science/wp/2...
> In a new paper published Thursday in the journal Science, Wu and his colleagues describe geological evidence for a catastrophic flood on the Yellow River in about 1900 B.C. — right around the time the “Great Flood” was said to have taken place.
There are tons of cases of non-myth non-bullshit sites in China, and yes, unrecorded in traditional history.