1. It *sounds* like a parasitic drain indeed, so definitely something to look at; is there any aftermarket components installed? e.g. OBDC reader? dash-camera? any modifications that could drain power? are you sure the car goes to sleep after you lock/close it?

2. Did you register the new battery?

3. The slow start could be a sign of the starter being on its way out -it is a common issue for a X5 that age- it happened to mine; it started behaving like that and after a few months it just died all of a sudden.

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E70 - 3.0si & F10 - 535ix
Previous Cars:
E34 - 525i, E39 - 530i, E60 - 530i