You could disconnect the air pump after starting a cold engine and feel for the blower to output air and simultaneously there should be no exhaust gas coming from the opposite end.

This graphic is from the E65 training literature (also from bmwtechinfo.com), but it should be similar for the E53 X5 with the N62B44 engine.

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2010 X5 3.5d: SOLD, but miss the torque...
2004 X5 4.4i: SOLD, but served us well