Everyone has mentioned all the normal things except plan on the seal in the trans where the wiring goes into it. (MECHATRONIK seal, #1 in the image below), normal suspension bits and pieces. The thrust arms if not replaced recently are toast front AND rear. Check all the parts in the suspension and replace everything at once, front and the rear, as it will make your ownership a happy one. All of this will bring back the new handling you expected. Replace all fluids (they are 10 + years old now), coolant, brakes, Diffs (front and rear) etc.
Real question is "Are you into the vehicle long term or short?" As that will determine your options and next steps. These V8 rockets are not cheap to own or maintain. Plan on one of two problem approach options: DIY (requires knowledge (see forum for insight), tools, and place for repairs. DIFM (do it for me) requires deep pockets and a indy shop for happiness.
If this is a short term relationship, then fix what makes noise or leaks and move on.
Reach out anytime to this forum as many of us will offer suggestions (some more helpful than others

). There is also a TON of tips, tricks and pit falls to avoid listed in the DIY Articles up on the top of the site. SEARCH FIRST post second if you don't find anything.
Bottom Line: Best vehicle purchase possible for bringing a smile by the mile, for the cost of ownership.
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2005 X5 4.8IS
The
Blue ones are always FASTER....
Current Garage:
2005 X5 4.8is
2002 M5 TiSilver
2003 525iT
1998 528i
Former Garage Stable Highlights
2004 325XiT Sport
1973 De Tomaso Pantera, L Model
1970 Dodge Challenger T/A 4 sp Alpine White
1970 Dodge Challenger T/A 4 sp GoManGo Green
1971 Dart Sport, “Dart Light” package
1969 Road Runner 383
1968 Ply Barracuda 340S FB Sea-foam Green