Your car has wiring in the luggage compartment for a phone, and it has a connector for an eject box.

If you check the connector used you may be able to fit the eject box. Early E39 cars had two connectors. Later the connector was standardised to a black 18 pin Quadlok. The latter is what you will need for the eject box.

In the luggage compartment, you will either have a 25pin DB25 connector or a 54 pin connector. The latter is what you want, but beware there were two incompatible pinout versions. You don't want the BITII version. Adapters are available for you to convert DB25 and BITII to the connector needed to fit a TCU (Post 2005) or ULF (post Gen 13).

With the eject box and TCU/ULF you will get bluetooth connectivity and charging.