The analog part of the DAC+ Pro can be powered independent from the power supply of the Raspberry Pi and the digital part of the circuit. However, a small modification on the board is needed:
You need to de-solder the resistor R14 and connect your external 5V power supply to the pin header P3 (left GND, right +5V)
Note that this modification voids the warranty. We recommend it only for experienced makers.