"HTML 5" is sort of a vague notion right now. AIR doesn't support "HTML 5", but it does support some of the features generally associated with HTML 5. Which ones are you looking to use?
I am looking for HTML 5 offline storage.
AIR has no support for HTML 5 offline storage as it uses the embedded SQLite database software. Here's a list of items which are, and are not, supported by AIR 2.5: