Bongo, before you start spending money...have you tried the pairing procedure? It's a 10 second solution where you:
1. sit inside the car
2. Lock the doors
3. insert key, twist (one click) and take out key straight away
4. Hold the unlock button and press 3 times on the lock button.

The car will lock/unlock itself to confirm the key function.

You can also youtube this procedure, very common and plenty of videos.

Good luck

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BMW X5 E53, 4.8iS - 2005
Professional Stereo/Nav with DSP (modified BM54 module) - Converted to Eonon GA5166X with Reverse cam
4-Corner Air Suspension - Converted to BC Coilovers