Mobil 1. My wife's 97 Civic has been using Mobil 1 for the past 5 years and there is zero varnish under the valve cover. Mileage is 166,xxx km (102,xxx Miles).
Fool proof isn't possible since we have too many fools out there that abuse their cars. But never a Bitoger ;-)
Good question that I don't have the absolute answer to because I don't have a lab to test oils. Sure wish I did. I "would think" that any modern oil available today from Supertech conventional up to Redline full synthetic will go 5000 miles without varnish. Obviously you have a better chance of pure clean engine internals with synthetic.
So, for my opinion (which it is only my opinion), I would run these oils to meet your goal of NO varnish in 1yr/5000 miles:
Mobil 1 EP (my favorite)
Pennzoil Platinum or Ultra
Redline or Amsoil
AS for conventional oil, I would venture to assume Pennzoil yellow bottle would be close to your requirements.
It depends how hard the engine is on the oil as well.
I've seen pictures of BMWs and MBs with Mobil 1 0W40 changes and the engines were spotless and there was no yellow under the valve cover. VWs on the other hand had some varnish.
Amsoil or Ultra for uber clean 1 year intervals at that mileage, IMO. Though, I doubt you'll go wrong with M1 EP or any other full synthetic.
But, you didn't exactly define fool proof beyond 1 year/5k mile change now did you?
...and ofc you haven't stated the app, etc etc etc. Oil itself is capable of many things, engines on the other hand? If it's a brand new engine, clean already I doubt you'll have any deposits/'varnish' worth noting.
The reason I suggest Amsoil or Ultra; as I believe others have already, is the lower NOACK and strong HTHS for most of their grades. This means probably less need for top-off over the course of the year as the base oils/TBN overall is very stout in those oils. I mean I doubt you'll get sever TBN readings for only 5k miles in a year, as it's enough use not to be a huge deal.
The only time TBN might be a question mark for a year at short total mileage is if those miles are all sever service. That is, short trips/cold starts/long-idle use, etc.
I recall someone that posted a run with ASM 0w-20 that had terrible remaining TBN at relatively short oil mileage use. The problem? 1/2 mile trips one way to work all winter as the majority of the duty/operating cycles.
Now, if the engine was clean does that mean it left a lot behind after such a run? Flip a coin, but you're pushing it. At the very least it may not be repeatable; i.e. run oil into ground in severe service and expect to be able to extend the oil interval but remain without any sort of visible 'dirty'.
Mobil 1 20W50 motorcycle.
I like the Aeroshell answer
because of the high flash point and ash-free additive package.
There are gas engine oils that would be very resistant to
oxidizing and nitrating as well.