I totally understand that situation because I have been through similar education in Taiwan about twenty years ago as well. Thankfully the history education here is saner now.

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.