l asked recently about fitting 15inch tyres to a metric size wheel, tyre size 220/55VR390, and all of the advice l received was against the idea and said it could not be done. The only option left is to replace the rims to take a 15 or 16inch tyre.What other BMW rims would fit a 1985 735i BMW?

For a 15'' you will want to find one with a 18mm offset, a 5x120mm bolt pattern, and put a 225/60-15 tire on it.
There are a lot more 16'' available, at least from Tire Rack. Then it would be a 20mm offset, with a 225/55-16 tire. The V in VR is a speed rating, and would be used for these sizes as well.

edit: l just put what tirerack listed for an offset. click the link.

Why 18mm offset for a 15 inch wheel M333? You can run anything from a 12mm to a 26mm offset with 20mm being the most common.
Like l said earlier it is best to simply find a wheel from an E34 5 Series or E32 7 Series. These have the correct offset, bolt pattern, & hub diameter.
You can source from any 5 & 7 Series except u will need hubcentric rings if sourcing from an E39 5 Series. 6 is & 8 is r also good sources but the 5 is & 7 is r more common & there is more selection.

if you replace the wheels with bmw 15 inch alloys, the car will look hideous as the wheels are too small, try one on and make your own mind up before you commit to buy, personally you need to be looking for wheels about 17- 18 inches wide, but then your still going to have the tyre problem. stick with the wheels you have as theres loads of tyres on ebay for bemmas

For cheapness, stick with the original sized BMW alloys, which will take 225/60 VR15 tyres, any wheel from the E23 7 series or E34 5 series will fit, maybe they wo not look so cool as huge pimp wheels, but you will find a set in a scrappy easily enough. You could go up to 17'' or 18'' on an '85 7 series, but the wheels and tyres will be expensive. Ask at a local alloy wheel supplier.

Other people have answered the tire size & offset issue. TO make this more simple just about all wheels with 5 lugs will fit(3 series wheels will not work). There is one issue BMW after a million years of using the same size center hole decided to make it just a smidge bigger, l think they changed over in 96. Its not a real issue but u have to go to a tire store & order up little rings u put in the holes to help center the wheels(10 to 20 dollars). Maybe u can find an online place to get them. Also even tho after market wheels r cool looking oftem they tend to be a big problem.

l take it you are swapping from expensive metric tyres,e34/e32/e39 models of bmw will go straight on they all have the same stud pattern and offset.including 16'' 17'' and 18'' alloys will fit.best bet is a set of bbs cross spoke off a e34 5 series with 225-50-15.pick up a set for approx £100.