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If you're not willing to learn or be adaptive to your customer' needs then you have no place creating websites as a profession

Its not me doing a HTML5 but does the website require is more of a question.

Using HTML5 or not makes no real difference for simple pages, so why wouldn't you do it? As far as I know it doesn't really have downsides.

If they mean something more than just HTML5, figure out what exactly they mean and decide about that.