Ford 500 2005 right piston will not recess completely

Hey Bradley....
Do they lock up right away.. or after a few minutes use(hot).. if they are locking up after usage.. they might need a complete bleeding and MAYBE the caliper pistons are sticking.If the pistons are sticking, this will require a complete caliper disassembly, cleaning, and replacement of the piston o-rings and a cleaning/polishing of the pistons. The brake system will HAVE to be bled completely afterwards.
This should clear the locking up issue...

A six cylinder in-line engine has a power impulse every 720 degrees/6 i.e. 120 degrees of crankshaft rotation. The crankshaft has six crank-throws placed at 120 degrees out of phase with one another, which can be arranged only in three planes. Therefore, the crankpin phasing is arranged in pairs. For heavy-duty diesel engines, seven journals and bearings are provided, at each end and between adjacent crankpins. For petrol engines only 4 or 5 main journals are provided. The firing order with the crankshaft arrangement shown in the attached figure is considered. With piston 1 at the top of the compression stroke, its opposite piston 6 is at the top of its exhaust stroke. Rotation of crankshaft through 120 degrees brings pistons 2 and 5 to their TDC and either one of these can be arrangement to complete a compression stroke. If piston 5 is arranged to be at the end of compression and at the start of its power stroke, then piston 2 must be on its exhaust stroke. Rotation of crankshaft through second 120 degrees positions pistons 3 and 4 at the TDC, so either one of these can be on the compression stroke. If piston 3 is made to be on compression, piston 4 must be on its exhaust stroke. A third rotation of 120 degrees brings pistons 1 and 6 back again to TDC, where piston 6 is arranged to be on the compression and piston 1, therefore, be on its exhaust stroke. A fourth 120 degrees rotation brings pistons 2 and 5 to their TDC. Piston 2 is now on its compression and piston 5 on its exhaust stroke. Rotation of crankshaft through fifth 120 degrees brings piston 3 and 4 to TDC. Piston 4 is on compression and piston 3 on its exhaust stroke. Final rotation of 120 degrees completes the 720 degrees displacement of crankshaft and brings the pistons into positions for the next cycle. This cycle provides a firing order of 1, 5, 3, 6, 2, 4. If the phasing of paired crank-throws 3 and 4 and 2 and 5 are interchanged, then a second equally suitable firing-order of 1, 4, 2, 6, 3, 5 is achieved. This arrangement provides excellent dynamic balance and evenness of torque, and is preferred for engines larger than 2.5 liters provided length is not a prime consideration.

Some pistons do not push back in, they wind back in. You can buy or hire the tool (here in the UK you can) but it can be cheaper to get a local garage to do it. Some wind the same way to retract, but others are handed and the left side goes one way and the right side the opposite.
I am not saying yours does this, but it might be worth investigating. Has the piston got what looks like something that a winding tool will fit to, or is it completely flat faced?
HTH

Try pushing in and rotating the piston clockwise at the same time. There should be slots or grooves on the face of the piston for this. You can use a C clamp and pliers if you are careful not to scratch the sides of the piston. You can buy or perhaps rent a special tool for this. Also, after the piston is retracted make sure the slot lines up with and engages the new pad properly

Your description gives me a suspicion the calipers weren't rebuilt to a very high standard.

The pistons don't turn as they are pushed out but mostly they have to be rotated or screwed and pressed in prior to fitting the pads.

Once fitted and bled ensure the caliper parking brake lever is hard against the backstop and then press the brake pedal hard a few times and the adjustment should be complete after removing any slack or free play from the parking brake cable.
With a new or quality rebuilt caliper a good parking brake should be obtained without needing to shorten the cable so the caliper levers are lifted from the backstops. That is the sort of compromise needed as the internal components become worn.

I have honestly never replaced brakes on a Ford Ranger but front disc brake pads are fairly simple to R & R. You either need a large allen wrench or a socket and ratchet. The socket size is probably 14mm or 9/16. You can use the tire iron and jack for your spare to remove the lug nuts on the wheel and jack up the truck. You should really use a floor jack and jack stands. Either way keep your body and limbs out from under the truck. Usually there are 2 caliper pins or bolts to remove. pull off the caliper and use a "C" clamp to compress the caliper pistons into the caliper completely and do not use anything but a clamp or you will never get it to depress. Keep the old brake pad in there on the piston side as a buffer between the clamp and the piston and it will help evenly disperse the pressure on the piston. Lube up the pins before you install them or they will be a nightmare to get out again. Vent the system by loosening the cap on the master cylinder to make the piston easier to depress. Let me know if I can help any further. Please rate me on this answer.

If it's like the 2003 The left-hand brake caliper piston retracts counter clockwise and the right-hand retracts clockwise.

1. Raise and support the vehicle
2. Remove the desired wheel
3. Loosen/remove the two caliper retaining bolts.
4. Remove the caliper from the wheel
5. Using a C-clamp, depress the caliper piston until it's completely recessed.
6. Remove the old brake pads
7. Install the new brake bads on the caliper
8. Reinstall caliper on the disc
9. Reinstall/tighten the calpier bolts
10. Put the wheel back on
11. Lower the vehicle.

*** When you are getting set let the car roll a few revolutions of the wheel to keep the pads off the disc. It will make it easier to get the caliper off.

If your having problems with the rear piston going in it because you need a special tool that allows you to turn while pushing.