Codes:
05 Knock Sensor or Knock Control Unit
08 Vane Airflow Signal (VAFSIG)
34 Idle Speed Control Solenoid Valve (ISC)
42 Turbocharger Boost Control Solenoid Valve (BOOST)
Code 5 and 8 are putting the car in limp mode and making it run rich.
What could cause multiple codes at once:
Grounds, the ECU/device grounds are white plugs that bolt to the cars body, they have multiple black w/greenish stripped wires going to them, there is one between the battery and inner fender, there is one on the passenger side in the same spot the power antenna motor is on the drivers side and there is a ground harness plug behind the ecu (easier to see from the drivers side). There are more but don't recall where.
The extra fuel is spooling the turbo up like launch control does on some cars.
Is it running like crap to 3000rpm, slow as can be, a little throttle or foot to the floor the car runs the same?
The only thing I have seen that will stop the engine from revving past 3000rpm and running like crap the hole time is ECU failure. This happened twice with 88-89 gt's and once with a 92 GT, symptoms where the same all three times, car ran like shit, wouldn't pass 3000rpm, runs so badly I never even shifted to 2nd gear out of fear (all 3 times).
The good news for you:
I couldn't pull any codes from the ecu, wouldn't even give the single ECU flash when connecting the test connector.
Also all three times the boost cut chip was fine, pulled them out and put them in another ECU and the cars ran the same as before.
1-Make sure the three harness plugs at the ECU are connected to it properly (disconnect and reconnect if necessary).
2-Reset the ECU, remove battery -, hold brake for 10 seconds, Reconnect the Battery -, reconnect test connector, turn the key to pull the codes. If the check engine light wont flash most likely the ECU is dead.
3-If the codes are still present than check the harness ground plugs I mentioned above, you can also look into the Knock sensor, Idle control solenoid and VAF, I know the VAF gets a ground signal through the harness, but for the idle solenoid and Knock I am not sure how they work, for the idle the ecu could send +voltage and Ground and simply vary or pulse the signal based on RPM or does the solenoid valve ground to frame the ECU sends +V to operate it and the solenoid sends +V back to the ecu for position reference? ... So using the workshop manual you will be able to find out if and where ground is sent to these 3 devices and which prong to check on the wire harness plug.
Find the plug, locate the ground pin in the plug, unplug the knock/isc/vav/boost solenoid, test with a multimeter + to battery 12V+, - to ground pin in the plug (Harness side), may have to turn the key to on.
Can't remember if you have any fuel modifications on your car, if you do that could explain the turbo spooling at 2000rpm and would tell me your base fuel pressure is set too high. The crappy adjustable FPR's I run default to 40psi at atmosphere (0 vacuum) no mater where idle pressure is set, running a 255lph pump I run 21psi idle pressure. Yes I can adjust Idle A/F's using the VAF bypass screw but that just adds air which means the engine is still burning the same amount of fuel, the idle will go up as air is added and the idle adjust screw must be adjusted and with all these steps it would seem to achieve proper A/F and proper idle with factory idle fuel pressure but millage went from 12mpg to 14mpg by running 21psi fp at idle. (94 octane, 3 cars 14 years no issues).