The 1989 model year was during the period that you will see described as the SZ cars, which means the car has hydraulics with mineral oil as the fluid, among many other things.
You may find it helpful to look at this page at the Rolls-Royce Owners' Club of Australia Post-War Technical library: http://rrtechnical.info/sz/05_sz.htm
In particular the changes that came with the 30000 series cars. I can never recall exactly when the series numbers changed, but look at the last 5 digits of your VIN and you will know whether yours in the 20000 series or 30000 series. I think you'll be at the tail end of the 20K series cars.
In my opinion, unless they are exceptionally carefully maintained, and even sometimes if they are, they will suffer more from lack of use than actual use. A car with 5K miles on it at 31 model years old has truly, barely moved. That also means that windows have not likely been put up and down, or the top up and down, and all sorts of other electromechanical items remain utterly un-exercised. I trust a car like this, that's cosmetically perfect but has not been used, far less than one that has far more use. There are kinds of maintenance that come as a direct result of use (as you know from your own daily driver) that simply do not happen on cars that are what I call "rolling sculpture."
If the car is still located near to where it was purchased you are in an area that has far more mechanics with deep Rolls-Royce experience than almost anywhere else in the country. One of the best things you could do is to have a very thorough pre-purchase inspection done by one of them, not because you don't trust your uncle, but because neither one of you can really say you can make an informed decision about what may or may not need to be attended to. A pre-purchase inspection can help to determine this, and also to come to a price determination. If you look in the RR & Bentley Parts, Repair, Restoration & Other Resources Compilation
at the shops in New York, New Jersey, and Connecticut and you can find several excellent choices for pre-purchase inspections.
It would be most helpful to have the SZ Chassis Number Derivation from VIN
so that potential assistants can give correct answers based on details that can only be known if a chassis number is known.