How can I connect five-wire pump harness to four-wire body harness?

Here's a wiring guide for the fuel pump on a 2000 Cadillac Deville: 1. Remove the fuel tank and access the fuel pump module. 2. Disconnect the electrical connector from the top of the fuel pump module. 3. Locate the wiring harness that runs from the fuel pump module to the car's electrical system. 4. Cut the wires on the old fuel pump module connector, leaving enough wire to splice the new connector onto. 5. Connect the black wire from the new fuel pump module connector to the black wire in the car's wiring harness. 6. Connect the purple wire from the new fuel pump module connector to the purple wire in the car's wiring harness. 7. Connect the gray wire from the new fuel pump module connector to the gray wire in the car's wiring harness. 8. Connect the black/white wire from the new fuel pump module connector to the black/white wire in the car's wiring harness. 9. Connect the new fuel pump module electrical connector to the car's wiring harness connector. 10. Reinstall the fuel tank. Note that it is important to follow the wiring guide carefully to ensure proper installation and avoid damaging the fuel pump or electrical system. If you are unsure about any step of the process, it is recommended to seek assistance from a professional mechanic or refer to the vehicle's service manual.

For the fuel pump motor the gray wire is voltage. The black wire is ground. The two wires on the left are for fuel gage sending unit.

There is a red wire close to the battery in the front. It's not connected to anything. Apply positive voltage and that will run your pump for testing purposes.

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Is it carved or efi??If efi do this::locate your throttle body,pull the air intake hose loose from the throttle body,spray starting fluid or carb cleaner into the throttle body opening, push the hose back onto the throttle body then try to start the car.If it starts & runs for a few seconds then dies,you've got a No Fuel problem.If it doesn't start at all,you've got a No Spark problem.If its a no fuel issue,turn the key on & listen for the fuel pump priming sound.If you don't hear it,check for a blown fuel pump fuse,defective fuel pump relay,a defective computer power relay or a tripped inertia switch.If they're OK,disconnect the harness at the fuel pump,turn the key on and use a voltmeter to test for battery voltage.If voltage is present,the pump is bad.If voltage isn't present,but its present at the fuel pump relay harness, there's most likely a short/open in the wiring harness between the FP relay & pump.You didn't list your vehicle info,so I'm unsure of which type ignition you've got.
Most no starts on a new engine are caused by a ground wire you forgot to connect,wiring harness not plugged in or a timing issue.

Did you check for voltage at the relay socket before replacing the relay ? Most relays have four or five pins , two should have battery voltage , one goes to the fuel pump an the last one is a ground supply from the PCM - powertrain control module - engine computer if you know what that is . If you look on the bottom of the relay it should have some numbers 85,86 , 30,87 ! 30 an 87 are the fuel pump side . 30 is battery voltage for the pump ! 85 is battery voltage an 86 is ground from PCM . VEHICLE RELAYS Operation Diagnosis Before replacing wiring harness test ! Check out these videos... Fuel Pump Electrical Circuits Description and Operation

Bad ground. It runs to the front of the car. You can cut it and ground it to the body. Make sure the battery to body ground is good also.

It was an upgrade you need to cut wiring harness and replace it with the new connection system .or it could be a problem with the fuel pressure sensor that plugs into the top of the pump wiggle the wires

Hello! The fuel pump, fuel pump relay, and the fuel tank pressure sensor are carried by a wiring harness to connectors that plug into the BCM...Outputs from the BCM are carried by wiring harness to there termination point and connect via plugs...Signals inter the BCM, are processed internally, and exit via connectors...Guru...Saailer

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Remove the bolts that hold the bed box to the frame, disconnect the rear light wiring harness and the fuel filler pipe. Set up a pair of saw horses or something behind the truck. Then have four guys to lift on all four corners and set the bed on the stand you have ready. The bed is heavy! And there is the fuel pump! Replace with the new and take care to put the wiring harness for the fuel pump back where it was. Replace the bed, bolts and connect the lights. You are ready to go! Takes about two hours if you don't break the welds that hold the nuts for the bed bolts loose. Good luck!

It should be four wires. Gray is power to the pump, Purple is gauge control, and two black wires that are ground. You should have battery voltage on the gray for 3 sec. after the key is turned on. Did you replace the plug-in to the pump when you replaced the pump? The pumps usually come with new plugs