An HTML email may contain all the the HTML tags. Specially important, even when redundant, is to use
<meta http-equiv="Content-Type" content="text/html; charset=UTF-8" /> (or whichever charset you want to use) to avoid potential problems with charsets on clients that don't read the headers, or do a post interpretation based on what they find on the email. Also specify encoding on the headers if you are programming the email.
About using HTML5, I wouldn't use it unless you are 100% sure about the software your clients are using and their capabilities. Some clients may have an up to date HTML engine but some may not. Plus some people just don't want HTML email and they only get the text version, in this case, parsers usually just discard tags and add some new lines, but there may always be surprises.
Of course, you can test if it works, or you can send both versions, text and HTML, so if one doesn't work properly, the user still has the other option.