I've only ever seen on manual (a 3ltr petrol) and I've worked on and driven more X5's than I care to remember.
Do not discount the 3.0 petrol!!! They are the most reliable by a long way and also not slow at all! They are geared to give decent acceleration so do not feel sluggish at all!
Drive one and see!
In general most E53's are tyred old scrap but there are some decent bargaines to be had.
They are like a big E39 touring are harder on suspension bushes, the bigger tyres are more expensive.
Watch for judder when braking, brake reaction bushes and warped disc are common.
Avoid the panoramic sunroof, they just f uck up. Check the boot well for water ingress, the battery, radio (if it has Nav) and compressor are there and it lowest point so water can f uck them.
Check everything electrical! Electric folding mirrors, central locking can fail.
Outer door handle mechs, normally on the drivers side, rear window regs, heater blower resistor can drain the battery, check for erratic fan speed.
Rear axle bushes, front brake reaction bushes, rear air springs and if it has double air suspension (normally on 4.6 and 4.

front springs!
Diesels are the usual M57 dramas like turbos, injectors, glow plug relays, oil leaks and the auto box's on the diesels are the most common to fail.
3.0 is an M54 so pretty reliable other than the odd sensor or oil leak.
The 4.4 and 4.6 V8's are an M62 so head gaskets, oil leaks, water cooled alternators and stretched timing chains.
The 4.8 is an N62 and a better overal V8 but again expensive water cooled alternator and some (cant remember which years) suffered with worn intermediate levers for the valve tronic (think N42!!) which is a pain to put right.
Seriously, if I were in the market for an E53, money no object would be as late as possible 4.8iS as they are quick, make a great noise and are normally fully loaded!
Being sensible it would be a 3.0 petrol for maximum reliability and repair costs.
They are not sluggish and not that bad on fuel, think low 20's which is what my mrs gets in my E46 330i auto touring.