No, there won't be any conflict, assuming both pages have a <!DOCTYPE>
. In fact, browsers don't even distinguish between HTML 4 and HTML 5.
More specifically, without a DOCTYPE a page will be rendered in quirks mode which can result in several major differences. In Internet Explorer, for example, the page will be rendered by an older implementation of the engine, resulting in several DOM and JS (as well as layout differences). If you're using JS to manipulate one frame from the other, then there's a chance something doesn't work the way you expect it to — the way it would in standards mode.
TLDR; use a <!DOCTYPE>
.