Both my power steering and brakes stopped working at the same time. I can still brake my truck, but only if I press har5d with both feet. There is no fluid leeking, and both the power steering and brake resivors are full. What might this problem be?

Steering and Brakes are totally unrelated.

Steering wheel, steering pump, steering rack, wheels.

Brake pedal, brake servo, brake calipers and discs.

Take it to a garage.

how power steering works
https://www.google.com/search?q=how+power+steering+works

How servo assisted brakes work
https://www.google.com/search?q=how+power+assisted+brakes+works

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Did you check STOP LP fuse 15amp. in the rear fuse block ? Do you know where this is. Fuse Block - Rear Under the rear seat, on the left side of the floor pan.
The STOP LP fuse in the fuse block - rear supplies battery positive voltage to the normally open stop lamp switch. When the driver presses the brake pedal, the switch contacts close. The battery positive voltage flows to the left stop lamp assemblies, to the right stop lamp assemblies and to the center high mounted stop lamp (CHMSL). The left stop lamp and the CHMSL have ground at G402. The right stop lamp has ground at G401.
Did you check for power at the stop lamp switch ? both in an out of the switch with brake pedal pressed ?
Did

What you describe could be warped brake rotors or bad wheel bearings. Doesn't sound like the power steering pump.

You have a leaking power brake vacuum (this is what you hear) operated power booster. Go to this link to read the procedure of removing and pacing the power brake vacuum booster

Did you adjust the brake light switch correctly? To adjust the brake light switch, first press the brake pedal down a few inches, then pull the switch plunger rod out of the switch toward the brake pedal arm, as far as you can without using excessive force. Next, return the brake pedal to the pedal stop position against the pedal stop and pull the brake pedal toward the rear to push the brake light switch actuating plunger rod into the switch housing limited by the travel of the brake pedal arm rear travel stop position. This procedure automatically adjusts the brake light switch correctly.
If the brake lights still don't turn off with the brake pedal released, check the brake pedal arm for sticking or binding that is preventing the brake pedal arm from returning fully to the pedal stop when the brake is released.

Yes, your brakes are boosted by the power steering pump rather than by vacuum. I don't think it's air in the system. More likely your pump has failed, but you can try bleeding the pump. Here is a procedure from autozone.com:

Observe the following:
Use clean, new power steering fluid type only Hoses touching the frame, body or engine may cause system noise. Verify that the hoses do not touch any other part of the vehicle. Loose connections may not leak, but could allow air into the steering system. Verify that all hose connections are tight.


NOTE Power steering fluid level must be maintained throughout bleed procedure.

1. Fill pump reservoir with fluid to minimum system level, FULL COLD level, or middle of hash mark on cap stick fluid level indicator.
   NOTE With hydro-boost only, the oil level will appear falsely high if the hydro-boost accumulator is not fully charged. Do not apply the brake pedal with the engine OFF . This will discharge the hydro-boost accumulator.
   
2. If equipped with hydro-boost, fully charge the hydro-boost accumulator using the following procedure:
   1. Start the engine.
   2. Firmly apply the brake pedal 10-15 times.
   3. Turn the engine OFF
   
   
3. Raise the vehicle until the front wheels are off the ground.
4. With key in the ON position and the engine OFF , turn the steering wheel from stop to stop 12 times. Vehicles equipped with hydro-boost systems or longer length power steering hoses may require turns up to 15 to 20 stop to stops.
5. Verify power steering fluid level per operating specification.
6. Start the engine. Rotate steering wheel from left to right. Check for sign of cavitation or fluid aeration (pump noise/whining).
7. Verify the fluid level. Repeat the bleed procedure if necessary.

Observe the following:



Use clean, new power steering fluid type only Hoses touching the frame, body or engine may cause system noise. Verify that the hoses do not touch any other part of the vehicle. Loose connections may not leak, but could allow air into the steering system. Verify that all hose connections are tight.
NOTE Power steering fluid level must be maintained throughout bleed procedure.

1. Fill pump reservoir with fluid to minimum system level, FULL COLD level, or middle of hash mark on cap stick fluid level indicator.
   NOTE With hydro-boost only, the oil level will appear falsely high if the hydro-boost accumulator is not fully charged. Do not apply the brake pedal with the engine OFF . This will discharge the hydro-boost accumulator.
   
2. If equipped with hydro-boost, fully charge the hydro-boost accumulator using the following procedure:
   1. Start the engine.
   2. Firmly apply the brake pedal 10-15 times.
   3. Turn the engine OFF
   
   
3. Raise the vehicle until the front wheels are off the ground.
4. With key in the ON position and the engine OFF , turn the steering wheel from stop to stop 12 times. Vehicles equipped with hydro-boost systems or longer length power steering hoses may require turns up to 15 to 20 stop to stops.
5. Verify power steering fluid level per operating specification.
6. Start the engine. Rotate steering wheel from left to right. Check for sign of cavitation or fluid aeration (pump noise/whining).
7. Verify the fluid level. Repeat the bleed procedure if necessary.

I know GM decided to run the brakes and power steering vacumm all off of the power steering pump on some of their trucks. This could really be a big problem because if your power steering quit it would stop supplying your brakes with vacuum to stop the truck. In my experience I would check out the situation with the steering pump. Change it for a new one. Don't take any chances on smashing your truck.

Had a very similar symptom on my 2005 Hyundai Santa Fe and I made a video of how I diagnosed and fixed the problem.

if this car uses the power steering pump to help with the brakes it is possible that the pump went out or possibly the belt broke as well.

Not a lot to go on! This truck is a diesel?????? If so check that your fanbelts are in good shape and adjusted propperly. That should fix it!