If you are looking for a real slim case, I would suggest Ozaki O!Coat Solid (0,30mm - 0.3 gr) for iPhone 5. I'm using it since I bought my device and it is really perfect. It fits perfectly and has perfect precise cuts. 0,30 mm thin. Comes with an Ozaki screenprotector which has better quality than I expected also. I'm keeping that protector on my device as well.
Please share photos of the case on your phone. Especially the front and the side view with the buttons. Also what is the material of the case? Hard plastic or TPU? Is the case a snap on that catches on only the sides or does it also offer top coverage?