A rather simple optics problem?

It is not a "rather simple optics problem", because in fact such a plane mirror with glass in front of the reflecting plane introduces an optical aberration, so that the answer is only an approximation (good enough for the eye but creates problems when working out wide-angle optical systems). To make sure we are on the same page with this, if the refractive index of the glass was 1, same as air, then the image of the object is 5.0 cm + 2.5 cm over the other side of the reflecting plane, or 15.0 cm from the object. If the refractive index is 1.5, then it is 2(5.0 cm + 2.5/1.5 cm) = 13.333... cm from the object. That is, the glass makes the reflected image closer than it would appear if the index was 1. At the other extreme, supposing the index is infinity. Then the image would appear as if it was reflected off the surface of the glass, or 10.0 cm away, even though the silvered plane is on the other side.