Honestly, what the blue blazes does HTML 5 have to do with responsive design, much less what advantages does it actually offer over using HTML 4.01 or XHTML 1.0 so far as that is concerned?
The answer, ABSOLUTELY NOTHING.
Responsive layout is CSS3, there is nothing preventing you from using it with the actual recommendation doctypes.
Given the halfwit loosening of the structural rules, re-introduction of old redundancies, creation of all new redundancies, and pissing all over document structure with the garbage allegedly semantic tags I cannot fathom why so many people keep singing it's praises; whenever someone calls it "the future" I can't help but think "REALLY? Looks like the worst of 1997 to me!"
But like most of the actual cool innovations of the past six to eight years -- CSS3, ECMAScript 1.6/newer, the new web API's -- they seem to be slapped under HTML 5's banner to try and hide the fact that the emperor is standing there bare for the world to see. You take those away and actually talk about HTML 5 as a markup specification, there is little of value to anyone who has more than two brain cells to rub together other than stuff for building crapplets (MANIFEST) or the new INPUT types.
Nothing like watching 15 years of progress being hung, drawn and quartered, burned at the stake, and then hoping we can bury it in secret so the WhatWG doesn't defile it's grave.