Thankfully, with iOS 7, it's now very easy to sync your iPhone 5s or 5c with your Gmail account. For the purpose, just follow these simple steps:
1. Open the Settings app;
2. Go to Mail, Contacts, Calendars;
3. Choose Add Account;
4. Now choose Gmail as the type of account you want to add;
5. You'll be prompted to enter your Google account details - enter them;
6. Provided you entered your details correctly, you'll be taken to a screen where you get to choose the items you want to have synced;
7. Activate the toggles for Mail, Contacts, Calendars and Notes to have them all synced, or just those that you wish.
And you're all set! Enjoy seamless syncing of Gmail, Google Contacts and Calendar with your iPhone 5s or 5c!