Chosen Solution

‘‘‘I ordered an power supply off an website but it did not come with the 5 wire attachment you have to detach from the motherboard of the PS4. I was wondering could you use the same on that’s on the old/bad power supply to connect it back into the motherboard???

Yes, there should be no reason why you couldn’t use the old wires and connectors, disconnect the connectors from the old power supply and slot your new one in as per this guide your power supply unit may look different depending on what model of PS4 you have.