There are specific extractor tools as they are so troublesome to remove. Fairly common to find in France as it's a diesel market and the M57 was used in the E46.

Extracteur arrache injecteur bmw 330D e46 320D Equipement Auto Loiret - leboncoin.fr

While you are at it, you should update your breather to the vortex type if you have the version with the mini replaceable filter (some call it a mini loo roll).

If your engine (X5 generally don't have them) has the intake swirl flaps, this is a ticking time bomb and you should remove them and install blanking plates.

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2002 Euro X5 (E53) 3.0 diesel (M57)
5 speed manual with UUC short shifter.
Pre-xDrive NV125 transfer case (chain & gears).
Factory Xenon headlights, Spyder LED tail lights
Updated vortex crankcase breather.
Motorsport dead pedal, factory fire extinguisher, factory first aid kit, factory F&R mud flaps, factory PDC

Bilstein B6 shocks F&R
Redline oil has replaced "lifetime" fluids (F&R diff, manual transmission, transfer case and P/S).
Dimple magnetic drain plugs in all compartments.