Can I exchange an iPhone 4 with an iPhone 5 without getting a new SIM? I understand that for certain iPhone models it is necessary to get a new SIM if I want to exchange them. 

If I have a 4S and want to exchange it with a user who has just purchased a 5, is this possible to do by simply following the same straightforward SIM-transfer procedures used to exchange (for example) a 4 with a 4S.
According to this article, the problem isn't just the size.


  It turns out, as well as a smaller size, the Nano SIM is reportedly
  15% thinner than the Micro SIM cards. So even if users cut the Micro
  SIM to Nano SIm size with a knife or nano SIM cutter tool, the Sim
  card would still be too thick to put in the iPhone 5.