Hopefully, as the other guys have stated, it’s just a battery voltage issue. I assume your E53 is a 4.4i with the ZF 5HP24 transmission?

You can do a quick test of ‘shift solenoid C’, without dropping the sump, by removing the 16-pin connector on the back of the transmission



and measuring the resistance between pins 4 & 16



It should measure 26 ohms.

If there’s a problem, shift solenoid C (or 3) is the brown-coloured one on the end of the row in the sump



Phil