Both need about 7 volts and I say about just to make sure with 7 VDC we exceed the regulator dropout voltage. You cannot apply 5 volts to the DC barrel connector or Vin and expect the board to work. A Google of Arduino Power circuit schematic should get you some similar images. You get above 5 volts and your chip is toast. The +5 volt pin is downstream of the regulator and there to apply an external regulated 5 volts. Anyway, just keep in mind both the Vin pin and external DC barrel connector are upstream of the U1 voltage regulator. Keep in mind that diode D1 will have a forward voltage drop of about 0.7 volt. Arduino DISCLAIMS ALL OTHER WARRANTIES, EXPRESS OR IMPLIED, Arduino may make changes to specifications and product descriptions at any time, without notice. This is commonly called a dropout voltage and why most documents for the actual Arduino Uno suggest about 7 to 12 volts for the DC barrel connector or the Vin pin. Arduino UNO Reference Design USB boot En TM Reference Designs ARE PROVIDED 'AS IS' AND 'WITH ALL FAULTS'. Keep in mind that voltage regulators of this type have an overhead voltage which means we can't supply 5 volts in and expect 5 volts out. Now note the DC barrel connector and the Vin are both upstream of U1 the voltage regulator. The Arduino Uno voltage regulation looks like the below image.
