On the iPad, a 5 finger pinch will bring you to the home screen. How can we replicate that function on iPhone?
It's not possible to configure this five finger pinch gesture on an iPhone without jailbreaking it. Currently there are no jailbreaks for iOS 7 (see jailbrea.kr for available jailbreaks).
If the iPhone is a device with a version of iOS that can be jailbroken, then this can be achieved after a jailbreak using
Activator (both installed through the Cydia app store). You can even assign custom gestures, like for example, a three finger pinch or a four finger pinch, for this action.