Surely, out of the billions of books that exist in the world right now, some will survive 5000 years. The Library of Congress is archiving many (but no longer all) tweets [1] and web pages. The British Library is similarly archiving tweets, podcasts, etc. The Internet Archive idem ditto, and many national libraries throughout the world are doing the same. If even a tiny fraction of that survives the next 10,000 years, there'll be much more remaining of the 21st century than of the 35th century BC.

[1] https://blogs.loc.gov/loc/2017/12/update-on-the-twitter-arch...