I forgot to add that the days of a "Thermo Limiter" fuse replacement and a $1.00 can of Freon (R12) are long gone. A/C systems are complex and WAY TOO expensive for a "try this and then this" approach.
Beyond check fuses, is the fan turning on, check the fan relay, A/C switch light on, you will need BMW specific knowledge tools and testers.

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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