Thats the rubber linings around the tail lights that let the water in ..IMPORTANT ,You need to change the rubbers ,in anyways.
Think most of us with older E53 (me included),had this problem.
From the pictures,You seem to have a lot more rust than usual,but you can only see the extent of the damage after you cleaned all the rust around it.
First cover up the bulb hole with by putting a clean cloth inside (you pull it out afterwards),so you dont get rust inside tail light.If you do ,you will have to vacuum it out .
Use sand paper and a "scratcher ",anything pointed,to remove the rust.If the damage isnt too bad,you may get away with using some solder to repair the damage.
Good luck