The part numbers for style 5s from an E31 are
36 11 1 181 187 & 36 11 1 181 888
You just missed the first few digits, but it looks like your wheels did come off an E31 so they shouldn't need hub rings. I have been running the same size tires for a couple years with no issues, so tire size isn't the issue.
You should get them re-balanced. I had the same problem and I just needed the front wheels re-balanced.