Active Directory is not based on X.500 and LDAP was directly created as an alternative to the DAP standard that is part of X.500.
While X.500 is a precursor to both of these things, and influenced both of these things, and both of these things interoperated with X.500, they are not X.500. X.500 is for all intents and purposes pretty much dead in 2024, although I did deploy an X.500 based directory service in 2012 and it's probably still alive and running.