Since there's a native calendar offered on iPhone 5,iPhone 4, you might wanna switch your Google Calendar you use every day to your iPhone 5 Calendar. Here are some tips for you to sync Google Calendar with iPhone Calendar:
To sync Calendars on iPhone, you need make sure that there are no iCal, Exchange or Outlook calendars to sync, because iPhone 5 Calendar can only sync with one single source.
- Open Google Sync via Safari on your iPhone
- Under Manage devices, you can see your iPhone, select it
- Check all target calendars to sync
- Select the Save button
- Back to the home screen: press the Home button of your device
- Go to Settings and tap on Mail, Contacts, Calendars
- Choose Add Account… under the Accounts section
- Tap on Microsoft Exchange
- Enter your Gmail account info under Email
- In Domain section, Input m.google.com
- Type your full Gmail address as the username.
- Enter the Google Calendar password
- Under Description, you can optionally choose "Google Calendar"
- Choose Next to input m.google.com to set the Server
- Tap the Next button again
Now you've synced your Google Calendar to your iPhone and can start using it!