Unfortunately I do not believe it's possible in fully-conforming HTML5 with just HTML and CSS properties. Fortunately however, most browsers do still support the scrolling property (which was removed from the HTML5 specification).
overflow isn't a solution for HTML5 as the only modern browser which wrongly supports this is Firefox.
Since the "overflow: hidden;" property does not properly work on the iFrame itself, but seems to give results when applied to the body of the page inside the iFrame, I tried this :
iframe body { overflow:hidden; }
Which surprisingly did work with Firefox, removing those annoying scrollbars.
In Safari though, a weird 2-pixels-wide transparent line has appeared on the right side of the iframe, between its contents and its border. Strange.
I tried scrolling="no" in my current browser (Google Chrome Version 60.0.3112.113 (Official Build) (64-bit)) and that didn't work. However, scroll="no" did work. Might be worth trying