It’s not really a case of does GroupMail Support HTML5 – it’s more of a question does the Email Client that your recipient receives this message in support it?. In general, using HMTL 5 in Email is not recommended at this point in time.
Some Email Clients support it and others don’t. For example :
Hopefully in time to come HTML5 will be fully supported across all email clients, but for now it’s best to avoid it when preparing your Email Newsletter.
As always, feel free to contact the GroupMail support team if you need any further information.