Note power supply is not GPIO. Two 5v pins are physically in the "gpio header" but they are not themselves a GPIO and no, you cannot set up a GPIO pin to "output +5V supply" in fact they'll fry at +5V.
I would encourage in not even using the GPIO pins at 3.3V as a power supply.
It seems you are powering the rPi using the official AC adapter, which is reasonable for prototyping. So you think about 'outputting' a +5V from the pins.
In production I would encourage the use of the +5V pins as "inputs" to the rPi, and then branch off your +5V directly from the power supply. As your question:
If that's not possible, would you suggest using a secondary board to plug the 5V wire while I keep connecting the ground and GPIO wires to the RaspberryPi?
I'm not sure what do you have in mind but in the lab I just plug the +5 pins with their own cables branched off from the power supply. For prototyping, the pi is just another devices. In production we generally end up with some PCB to keep the thing tidy. I guess that could qualify as your 'secondary board' but I'm not quite on the same idea.