running 5e OSR-style without changing any rules

I know what you're saying - "just use a game actually meant for this!" But maybe you game with people you like IRL and who don't want to learn another system. The truth is that you can run things in a more old-school style without changing any player-facing rules.

As with any campaign style, you want buy-inv - such as to the idea that you're running a sandbox campaign where character death may lack individual narrative heft, in which challenges are not guaranteed to be fair, and in which lateral thinking goes a long way. The goal here isn't to sneak in OSR play to people with no interest in it, but to work with the fact that many groups don't want to learn a whole new system specifically.

Ask "how do you do that?" when players declare skill use

GM: "There's a pie in the middle of a room, surrounded by a bear trap."

Player: "I use Sleight of Hand to disable the trap. 18! Does it beat the DC?"

GM: "Hold your horses - exactly what are you doing to disable it?"

Player: "Hmm, I throw a stick on the bear trap to activate it."  

GM: "Success! The trap snaps shut."

You know already know this: play the world, the answer is not on your character sheet, blah blah blah. But in my experience (especially with new players) this doesn't require the lack of a skill system or anything, it just requires you to remind them to describe the physical actions they're taking and to engage with that.

Encourage use of automatic character generators

It's a trivialism that character creation needs to be easy in order to allow comfort with lethality. The traditional solution to this is to make character creation simple, but the 5e market is so large that there's also a lot of tools.

As someone who hates character creation minigames but is in a 5e game with friends, the straightforwardly named https://fastcharacter.com/ has been a godsend. I just specify the level and anything else I want to determine and boom. 

Giving access to devices like these doesn't mean players who enjoy the minigame can't engage in it - but it does mean that they don't need to feel like every character is an irrevocable investment.

Use any XP system other than XP for combat and set milestones

Does this count as changing rules? I don't know, but as elegant as say XP for gold is or whatever, I think that really XP for combat and "XP for this particular thing the GM has in mind" are the most fatal to open-ended risk-reward play. You can use just about anything else (handing out cards with XP for possible quests, actual XP for gold/exploration, leveling up arbitrarily when people feel like it's time to out of character or after a certain number of sessions, leveling up when people surprise you) and it will avoid the main problems.

(Does this count as changing the system? IDK, but in my Curse of Strahd campaign nobody complained when I gave them checklist XP adapted from Into the Depths.)

Use GM-facing procedures like morale, reaction roles, and hazard dice

That's not changing the rules either!

Just use bears

More generally, don't engage with anything mechanically you don't have to or that doesn't have a meaningful payoff. Be sloppy and arbitrary about stats, if there are players who are sticklers about e.g. tripping rules or whatever let them be the resident expert and defer to them on that, and so on.  

interleaved spark tables

Sometimes you want things that are related.

emoji spark table from Lenormand

Lenormand is 36-card oracle deck - that is to say, a d66 spark table. Just about every card is iconic enough that there's an emoji for it, and plain enough that you can guess reasonably enough at its meaning. In the few cases where there wasn't an emoji, I took one that approximated suggested meaning (swords crossed for whip) or which felt right even if the associations were different (dove for stork.)

5d hexcrawl with multiverse timetravel

Imagine your standard hexcrawl. That's 2D - north and south. 

But what if you've got the underdark, as in Veinscrawl? (Notably, most long-form treatments of the underdark treat it as divided into vertical region that progressively weirder the lower down you go.) Then you've got your three classic spatial dimensions, so we're up to 3D. (This also lets you throw in your cloud giant castles and what-have-you.)

Take the conceit of the more recent editions, that sideways from our world is the Feywild, where everything is more alive and vibrant, and in the other sideways is the Shadowfell. 4D! (I know what you're thinking, and to answer your question, per the 4e underdark book the intersection of the underdark and shadowfell has the supremely stupid name of the Shadowdark, not the equally stupid name of Underfell. The name of the intersection of feywild and underdark isn't funny enough for me to remember.) 

And if you have calendars, not just maps, that's 5D.  

Some additional things that you can use to play around with this:

• Time passes more quickly in Faerie. The way I'd be inclined to play it is that the Feywild has the same seasonal calendar as our world, but it's just the same year over and over, so that if you enter in September 23rd our time, and stay in the Feywild from September 25th, you'll exit into September 25th - but it might not be of the same year. (The feywild is also more full of glittering treasure hoards, and you can get the equivalent of a full night's sleep by just taking a breather there, so time spent is more valuable as well.) 
• Time passes more slowly in the Dolorous Lands. You can spend an arbitrary amount of time there and when you exit, it will be the next 4AM or so. However, you can't rest there; at least, not meaningfully.
• Especially with a good downtime system, this works for games where not everyone is going to be able to make it to every session. 
• It also might work well with a very long-term calendar, NPCs that have some branching futures (like these), some kind of domain management...

(See also.)