Welcome to the community!
Adding a few items to consider to an already-great list from previous suggestions.
- Check all service records
- N55 is generally a reliable engine. Very small percentage of N55 engines were affected by excessive connecting road bearing wear. It can be identified by a faint "clickity-clack" sound at idle speed. BMW dealer can perform analysis of motor oil and detect an excessive amount of metal shavings. It's a rare problem.
- Inspect all major seals for any leaks, i.e. engine, transmission, differentials
- Inspect radiator for any damage by road debris
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