I'm in the same position and I've personally looked into:

Jag S Type R's 2004 and up do something's come up for 5k earlier cars 3.5 to 4k......4.2 supercharged v8 420bhp later car is considers to be better and didn't suffer gearbox "lerch" fault on earlier car

On a more sensible note 05 to 07 Mercedes EClass 280 or 320 cdi SPORT, so you get the leather,nav,command, air suspension etc etc 07 plate are face lift and considered to be better but most of these are 160k+mileage low mileage ones don't seem to come up

Jeep Grand Cherokee 3.0 CRD 05 plate loads around for 5k and still mate that shape right up to 2011

I've looked into Audi A6's but after deciding I only wanted a 3.0 tdi Quattro le mans they got right out of my price range lol

BMW 330d E90 do some times come up for under 5k but no I Drive or leather

You might find a cheap Range Rover for 5k on maybe 02 plate

Plenty of BMW X5's for 5k too but hear there problematic