Ruff idle cuts out under throttle and back fires

How does it idle in park , does it run ruff or smooth? Are any lights lit on the dash , check engine etc. ? Could have a partially plugged IAC air passage .idle air control (IAC) valve ! The engine computer uses the IAC to control idle , when under a load such as when put into gear the computer raises the idle ! It does this by allowing more air to by pass the closed throttle into the engine raising the idle ! If these air passages clog they restrict the air flow an cause a idle problem ! Now if it runs ruff at idle in park you could have vacuum leak ! Rough Idle How to Fix Ford Taurus Engine Stalls at Stop Signs

have you gone over the throttle body and changed the idle position solenoid. They go bad and that acts like a cork , when it is stuck. It creates the air bypass , when you are idling. Take the intake snorkel off and look at it, clean it. take off the throttle body and you will be amazed at how much crud is under the butterfly plate. That crud gets into the throttle position sensor and the idle solenoid valve. I changed those sensors ( everything is $40.00 each for those ) and all idle issues went away. Have not been back for 2 years. Remember that fuel injected engines have an air pedal. it's not a gas pedal. If air is cut off at idle the computer can't compensate for it beyond a certain point. If it is running rough, then you also have to look at loose wires, spark plugs, head gasket integrity.

Check the air filter is clean, and the ignition for correct operation. The plug indications are that the engine is running rich (too much fuel) or that the ignition spark is weak.

Firing order is same for 5.0L or 5.7L

V8
1,2,3,4, Pass Side,front to back
5,6,7,8, Driver Side,front to back

1,5,4,2,6,3,7,8

Clean MAF--CRC MAF Cleaner
Clean Throttle plate--CRC Throttle Body Cleaner

You're probably ready for some engine internal maintenance Timing chain, valves leaking, you know. Almost 300000 miles, Wow

double check your firing order and make sure all wires and hoses are plugged in good. when you pulled the push rods out did you make sure they went back exactly where they came out because there are 2 different lengths.

you must have the throttle at full at all times when under load driving and mowing, back fire is do to much fuel. if your running throttle at full than look at the carburetor and then the wiring (short)

ICM idle control module, loc throttle body, it may be dirty, remove clean or replace, its easy..

use carb cleaner spray on the inside of the throttle body.

use super unlead only to prevent buidup.

cold engine only.

hope this helps
thank you
jm