Well the diameter of the 185/55/16 is 610mm and diameter of the 185/60/15 is 603mm, circumference of 185/55/16 is 1916mm and of the other is 1894mm.
So, while not ideal, you could probably drive with the “spare” for some time. However, it is not ideal and difference in wall height would affect handling, also, if you had an accident while driving with mismatched tyres your insurance cover could be problematic. The tyre pressure alarm will certainly warn you that something is wrong - it uses relative circumference as a measure.