For some time I had been baffled why my new iPhone 5 did not include my all my Google Apps calendars, even though my old iPhone did. I went through the standard synchronization process, and still only the main calendar showed up in the list.
After seeing that many people had the same problem, I tried a variety of suggestions and found that the following works.
Create a new Gmail account using the Google Apps credentials. Turn off the Mail option in the account settings, but leave Calendars and optionally Notes on. Contacts are not available, so we will create another account for that. Use the new Google “Syncselect” website (https://www.google.com/calendar/hosted/your_google_app_domain/syncselect) option to select the calendars that should be synced (Google support reference). Only the calendars that are checked on this screen will be available in the Calendar app.
If you want to synchronize your Google Apps contacts with your iPhone, then create another Exchange account using Google Apps credentials. Turn off the Calendar option, as that is handled above. Turn on the Contacts option. Turn Mail on or off depending on how you are handling your Google Apps email. If on, then mail will show up in the iPhone Mail app, or turn off to use the Google Apps Mail shortcut app (which I prefer).