More than that, HTML5 specifies how browsers handle "broken" HTML. There's a super-precise algorithm that dictates what to do for unclosed tags, how to fix up the DOM for incorrect nesting, specific fallbacks/behavior for invalid attributes, and so much more. I would say this algorithm, along with its element/attribute-specific components, are where most of the HTML5 effort was applied, and continues to be such for newer Web APIs.

Browsers "trying their best" was like half of the Browser Wars, and what HTML5 was largely created to address. The other half being nonstandard ActiveX crap and IE-specific JavaScript.