AJAX is just a buzzword for integrating HTML/XML, CSS and JavaScript so the answer is yes as there are no actual requirements for using AJAX, though you do need to know that most browsers do not support HTML5 effectively and it is still not even out of draft / beta stage so trying to implement it would be questionable.
The only reason that HTML 5 doesn't currently work with Ajax is that current browsers don't support HTML 5. If you can lay your hands on a copy of IE32 or Firefox 25 then you might have more luck.
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