There are default apps on the iPhone 5 (and the others I'm sure). How do I remove them off my screen? Such as the default Mail client? I have my own that I use and like.
Most if not all of Apple's own apps aren't removable like apps you download from the App Store. The only way to get them "out of the way" is either put them all in a separate screen, or put them in a folder (by dragging one over the other to create such folder) and then keep them there or drag the folder itself off screen (to a screen you don't use and don't have any other apps on)
To drag applications, either to change their placement or create folders, tap on any app and keep holding until they start to "shake". Press the Home button to turn off this mode.