Why does an arduino need 7V if it uses 5V?
That 7V is fed to an 7805-style voltage regulator, which provides the 5 the Arduino is running on. You could apply 5V to the appropriate pin directly, but


it must be a real stable 5V (not some wacky unregulated wall-wart)
you'd loose the current limiting of the 7805
the 7805 in the Arduino must be protected by a reverse diode, check the circuit