Yes, you can use HTML5 templates with Sitecore, I am doing so now. You will want to remove the XHTML validation from your workflow. To do so navigate to: System -> Settings -> Validation Rules -> Global Rules
Scroll down to workflow and simply remove the Full Page XHtml rule as shown here:
You might go to the next level and create your own HTML5 validation rule... or (fingers crossed) Sitecore will be creating one soon.
You can also reference Stephen Pope's answer - that's where I learned this handy trick.