The iPhone 5 does have the space to add a SIM card, but it has to be a Nano SIM Card which is smaller than most other types of cards. In order to open the SIM card tray on your iPhone 5 you need a special SIM card eject tool, or a regular paper clip will also work just fine. You will find the tray on the right hand side of your iPhone, then push the SIM card eject tool or paper clip into the small opening to pop open the card holder. From that point you can access the card that is all ready in there or add a new card.

Source Apple Support