You should activate the standby mode in the COMAND system. Not sure what year you have and if you have COMAND, but at least the 2019+ have a standby mode. It turns everything off, including the online services so the battery doesn't drain. If you have COMAND, mBrace or Mercedes Me connect are essentially constantly active and maintain a connection so that you can get status information from the car and do things like lock/unlock remotely. That will eventually drain the battery. After about 3 weeks I start getting battery critical warnings for my C63S through the Mercedes Me app if I don't turn on standby mode. I was traveling for 9 weeks earlier last year when I still had my previous car, an Audi RS5 and I hooked it up to a battery tender, just to make sure the battery doesn't go bad while I'm away.
I would also properly inflate your tires, preferably to max load recommended pressure, so that you don't get flat spots from the tires not moving for 5 weeks. Should be OK, though. I've been away for 4 weeks in the past w/o doing anything special to my cars and there were no issues.