Low voltage at fuel pump on 2005 new fuel pump no pressure. bench test good but no pressure in the truck. Pump will pump fuel when hooked strieght to 12 volts. I am only getting 10.32 volts at the connection at the fuel pump. Is there a fuel pump relay on this truck. It is not listed in the owners manual.

In the past, I bench tested a fuel pump that I new was faulty. It was a waste of time. The fuel pump ran up a storm on the bench not on the vehicle. With pump on the vehicle, I used a gage and checked fuel pressure, none. I checked for good voltage and ground at the pump, that was good and no pump action.
The pump in question, I cut it open, the little brushes were wore down to the nub. A new fuel pump fixed the problem on that vehicle.

Your fuel pressure is really low.

Did U check the power in the pump conection?
Check the filters.
Conection malfunction!
Sametime can be a dirty fuel tank .

Disconnect the wire connection to the fuel pump, turn it on and test for 12V (or whatever your car battery voltage is) at the leads coming from the battery. If 12V is present the problem is the fuel pump. Test the continuity of the pump circuit at the same time (no power on for this test). set VOM to resistance attach to both leads going to pump. If reads 0.00 continuity is OK. If no reading pump circuit is open, pump motor is bad. I have had them bad right out of the box. Good lesson to learn whenever possible, ALWAYS bench test new parts before installing.

No fuel pressure means the pump is not running. Check the pump fuse and if it is good, find the pump relay and check for power going to it on the thick (red?) wire. If it has power there hook a meter or test light to the smaller power wire, have someone turn on the key while you watch the meter or light. It should read voltage for a few seconds.If that is good check the power wires going out from the relay to the pump. Same drill with the meter/light. If there is no power coming out from the relay it is a bad relay.

What's the fuel pressure ? Hook up a fuel pressure gauge an test it yourself . fuel regulator ??? It's a fuel pressure regulator . I was starting rough and I had a diagnostic done. "They" said it was the fuel regulator.
Hard starting - not starting rough . What year is the truck , what engine does it have . If they don't know for sure what's wrong you better try another repair shop that know's how to diagnose .
Electrical problems can lead one to believe the fuel pump is bad . Doing voltage drop testing on the electrical circuit is a very good test.
Testing Electric Fuel Pump Problems with Voltage Drop Test
Plus doing current testing can pin point a bad fuel pump .
059 Engine Hard to Start or No Start Current Test for Fuel Pump

Check for a fuel pressure regulator. If you are testing the pressure at the end of the line, the fuel has already passed through the regulator. I'd be willing to bet the pressure coming from the pump(s) directly is up to snuff.

if power fine and no fluctuation than the pump itself is problem or problem with filter new doesnt mean cant be faulty also listen to pump if hum goes high /low than pump is surging and is faulty if pump stays steady and pressure test is steady when teted before fuel filter than problem with filter or line

glow plug relay should be on the front are rear of intake.you have a mechanical low pressure pump on the passenger side low near the front. or a electric low pressure pump on the starter side. your truck should have the low pressure electric pump. to check fuel pressure you disconnect the out let line to do a out put test.on the electric low pressure pump.put out let line in a container.crank engine for 20 to 30 sec.you should have a good flow of fuel no dribbles.if dribble replace low pressure electric pump.the mechanical low pressure pump out put test you disconnect fuel line from the fuel filter inlet line.disconnect wire at fuel injection pump electric shut off solenoid .place the fuel line in a container. crank engine for 20 sec. fuel flow looks good.pump is good .if dribbles.replace mechanical low pressure pump.to check glow plug relay you need a .diesel repair ford manual to show you where to put a test light to check the relay.WEAR SAFETY GLASSES WHEN WORKING ON DIESEL ENGINES.DONT DISCONNECT THE INJECTION PUMP LINES WHILE ENGINES IS RUNNING.THE FUEL PRESSURE IS SO HIGH SPRAY IN YOUR EYE CAN CAUSE BLINDNESS.GET IN SKIN OR SORE CAUSE BLOOD POISON. CAN ALSO CAUSE A FIRE BE VERY CAREFUL.

try hooking up a fuel pressure test gauge to fuel rail pre filter and post filter and rev truck to 2500 rpm what is fuel pressure ?
next using a vacume pump attach to fuel pressure regulator pump up while engine is running only pump up to 8 psi to see if pressure changes if not replace pressure regulator .
it could also be ur speed sensor switch on overdrive transmission
good luck with it