If your iphone is non jailbroken than you can update it via OTA otherwise use Itunes to update. Geveysim is working on ios 7 (call, text, edge, gprs etc) but USSD Codes (*# commands) may not work.
STRAIGHT FORWARD TUTORIAL:
CAUTION: Once you update to ios7, currently there is no way to downgrade.
To update via Itunes.
*Download the latest version of itunes.
*Backup your iphone.
*Download the CORRECT (Because there are 2 models of iphone 5, model number is written on back of your iphone) firmware file (.ipsw) from the link
Download iOS 7.0.3 IPSW For iPhone, iPad, iPod touch [Direct Links] | Redmond Pie
*Attach your iphone to PC.
*On itunes while iphone is connected press Shift+Update.
*Thats all. Restart your iphone to activate, if required. Enjoy your new iOS7.
FEEL FREE TO ASK ANYTHING