Look like Style 63s to me:
front: 9"x19", offset is 48
rear: 10"x19", offset is 45
from this site below; just use top tab, plug in E53 and the wheels
are listed. Click on your or any wheel shown and it gives you the
stats:
http://felgenkatalog.auto-treff.com/
A very good wheel/tire comparator:
http://www.bigcustomwheels.com/rt_specs.jsp
Let it load and plug in your current wheel/tire specs on
left model and then you can play with potential new wheel
sizes/offset etc. to see how it fits.
GL,mD