The break tags are not needed in that situation but it has nothing to do with XHTML. If they were XHTML break tags they wouldn’t have the space before the slash that was only ever needed for Netscape 4.
Break tags for XHTML5 are written as <br/> and provided you don’t need to support IE8 (which doesn’t understand XHTML) you can quite reasonably use XHTML5 instead of HTML5 for web pages just by ensuring all tags are closed and by changing the MIME type.