use html5 in facelets/jsf2

I am using this in my server-side "index.xhtml" (I saved this file with suffix *.xhtml):

I am using this in my web.xml:

I get this warning from JSF when going to my browser and clicking "index.html":

When putting the needed xmlns to xhtml, then no warnings appears:

However, the rendered client-html looks like this (which is not clean html5-code):

instead of this (which is clean html5-code):

When changing my javax.faces.DEFAULT_SUFFIX to .html

and renaming my server-side-page to "index.html" (Now, I saved this file with suffix *.html),
then facelets cannot render the page at the client side. That means, the client gets the facelets-site without transforming it to appropriate (x)html.

Should I ignore the warnings or is there a better (clean) solution?