I recently bought a set of 5.5" x 13" Octavos, and, with 185/70 tyres they fit on my Touring with no problems...yet. I have not really driven the car in earnest. For 20 years I rode around on the E21 Alpina style alloys with no problems and the Octavos appear to be the same spec basically.
I did have to buy a pair of 2mm spacers for the rears as the "aftermarket" looking centre/hub caps didn't clear the end of the hub.
Your hub caps look like the real deal, so you probably won't have that problem...…...got any more???
Cheers,
Les
Forgot to mention - I have Bilstein HDs & (I think) suspension techs springs, so slightly lowered.