I honestly think the basic Fate point economy could be bolted on to almost any system, as long as certain other assumptions are ported in with it.
Your high concept should probably include your species and class, with an extra adjective or so: "Devious Elven Ranger" or "Human Wizard of the Order of the Star".
Invoking an aspect gets you a reroll or a bonus to the dice roughly equal to a standard deviation. (For a d20, that'd be about +6.) In 5e, I'd probably let it eliminate disadvantage if desired instead. Given that in 5e, damage is rolled separately from hitting, you could potentially invoke on damage rolls as well!
Missing the DC of a roll by 1 (or possibly a bit more, maybe 1-3) might give you a Boost.
Along with the economy, it would be highly desirable to import the idea of "success at a cost". And the GM would want to apply aspects pretty freely to NPCs, areas, and scenes.
Done, pretty much. I haven't tried it, but I don't see any reason why it wouldn't work. You could even give people Consequences when they get hurt enough (0 hp, probably - but 1/2 hp might be a Minor), or something dramatically awful happens.