What are the probable causes of DTCs P0171, P0174, and P0500?

There is a mixed bag of codes that are unlikely to occur at the same time in a well maintained vehicle - if the codes are all genuine separate faults the car is likely in a very poor and much neglected condition. A couple of the codes could be genuine but it is most likely they have a common cause and the only thing common to those faults is the PCM.
An explanation of those codes will be found on the links below...

https://www.obd-codes.com/p0562

https://www.obd-codes.com/p0500

https://www.obd-codes.com/p0507

https://www.obd-codes.com/p0174

https://www.obd-codes.com/p0171

https://www.obd-codes.com/p0700

https://ricksfreeautorepairadvice.com/u2106/

I suggest you obtain a wiring diagram and check the supplies and grounds to the PCM and if ok have the PCM checked before spending any more money.

P0300 - random misfire , P0171 & P0174 lean code's . All of this means you could have a bad vacuum leak ,low fuel pressure ,clogged fuel filter , Mass air flow sensor problem .
Ford 150 P0171 P0174 Trouble Codes vacuum leak water test
Low fuel pressure causing P0171 and P0174 trouble code

code p 0171 refers to system too lean bank 1===causes --intake /exhaust leak---AIR system---MAF/VAF sensor---fuel pressure/pump---injector/s---HO2S
In this case I would suspect the heated oxygen sensor (HO2S)
then check fro a cracked flex section in the exhaust before the cat converter
code p 0174 refers to system too lean bank 2---causes intake /exhaust leak--fuel pressure/pump---injector/s---AIR system---hose connection/s

Please go to this site on pc, It will tell the meaning of the codes and detail info. God-Bless! ( repairpal.com/obd-II-code-po171-and-po174.) Clink on first link, when page comes up.

Hi Guy,here's a link to your codes. P0171 and P0174 OBD II Trouble Codes

Smoke testing for codes P0171 P0174 - YouTube

? 5:48
www.youtube.com/watch?v=kZsqEfP-5zM
Jan 18, 2011 - Uploaded by realfixesrealfast Smoke testing for codes P0171 P0174 .... I have a 1995 ford mustang gt 5.0 and it keeps having a Fault code 176 pop up. ....Ford Explorer P0174 code intake air leak check engine light by froggy - Duration: 16:11. by froggy ...

HI the DTCs you listed P0171 P0174 are lean fuel trim codes. I see alot of faulty O2 sensor cause these to set along with leaking intake gaskets and fuel pumps. Without being able to see actual data from the trucks system its impossible to pin point the cause I can only give what issues we see the most of

Fuel Sys, Driveability, Filters (Air & Fuel)
2006 CHEVROLET COBALT

02/01/2006 ELIMINATION OF FUEL FILLER TUBE FLAPPER DOOR 03/01/2006 ERRATIC FUEL GAUGE READINGS 06/01/2006 USAGE OF E85 FUELS IN GM VEHICLES - REVISED 06/01/2006 L61 ENGINE MALFUNCTION INDICATOR LAMP (MIL)/SERVICE ENGINE SOON (SES) LAMP ILLUMINATED WITH DTC P0171 "FUEL TRIM SYSTEM LEAN" SET 07/01/2006 TOP TIER DETERGENT GASOLINE - DEPOSITS, FUEL ECONOMY, NO START, POWER, PERFORMANCE, STALL CONCERNS - REVISED 07/01/2006 USE OF E85 FUELS IN VEHICLES NOT CERTIFIED BY GM AS BEING FLEX FUEL COMPATIBLE / AFTERMARKET CONVERSIONS OF VEHICLES TO OPERATE ON E85 FUELS 09/01/2006 397.pdf&btitle=2006 CHEVROLET COBALT&yr=2006">GM FUEL SYSTEM TREATMENT PLUS, FUEL SENDING UNIT CORROSION AND FUEL SYSTEM DEPOSITS - REVISED 11/01/2006 940.pdf&btitle=2006 CHEVROLET COBALT&yr=2006">ERRATIC FUEL GAUGE READINGS - REVISED 03/01/2006 USAGE OF E85 FUELS IN GM VEHICLES - REVISED 12/01/2006 TOP TIER DETERGENT GASOLINE - DEPOSITS, FUEL ECONOMY, NO START, POWER, PERFORMANCE, STALL CONCERNS - REVISED 01/01/2007 EMISSION RECALL - ENGINE FUEL INJECTORS - REPLACE 01/01/2007 LSJ, L61, LK5, L52, LL8 ENGINE - REDUCED ENGINE POWER, MIL/SES LIGHT, DTC P1516, P2135, P2138 02/01/2007 MULTIPLE DRIVEABILITY SYMPTOMS DUE TO CLOGGED FUEL INJECTORS, MIL/SES DTCS P0171, P0172, P0174, P0300, P1174, P1175 - REVISED 03/01/2007 MULTIPLE DRIVEABILITY SYMPTOMS DUE TO CLOGGED FUEL INJECTORS, MIL/SES DTCS P0171, P0172, P0174, P0300, P1174, P1175 - REVISED 05/01/2007 MULTIPLE DRIVEABILITY SYMPTOMS DUE TO CLOGGED FUEL INJECTORS, MIL/SES DTCS P0171, P0172, P0174, P0300, P1174, P1175 - REVISED 06/01/2007 <A href="http://arrc.epnet.com/autoasp/data.asp?sid=122357497&uid=s9193090.remote.autorefctr&type=pdf&ff=082000

po171 is system too lean,bank 1,po174,is system too lean,bank 2,It sounds like a fuel pressure problem.