How do I get rid of game center on iPhone 5 home screen
You cannot get rid of Game Center on the iPhone 5. This app is pre-loaded on the iOS. However, you can create a folder of unwanted apps and move it to the last screen on your iPhone 5 where it will not both you. Go to http://ipod.about.com/od/iphonesoftwareterms/qt/Delete-Game-Center-App-From-Iphone.htm for more information.
You cant, it will stay there forever
tap it twice and it will show delete.