Exactly,
5000 year history, big whoop. Technically, my 1/8th Native American side has a good 15-40K year histoy.
China likes to have their commie cake and eat it too. They claim 4000 years, but had a "Cultural Revolution" where they rejected 3940 years of that history.
Chinese Civilization started around 1949.
Though what you say are also true, the typical notion of "civilization" begins with writing and continuous records of literature/history. In this sense, Chinese civilization is indeed 4000-5000 years old. They are still using their hieroglyphic writing system. A college educated Chinese knowing only the Chinese language can read original source documents dating at least 2000 years ago. This is not possible for the English who are not trained in Latin or Greek, much less the Native Americans. So Native Americans don't have 15-40K years of continuous civilization.