Engine runs fine when first started, then engine throttles high then low, high then low

There are a few possible reasons why your 4M41 2003 model might be cutting and idling high after 5 minutes. Clogged fuel filter: The fuel filter removes impurities from the fuel before it enters the engine. If the fuel filter is clogged, it will restrict the flow of fuel to the engine, which can lead to a variety of problems, including cutting and idling high. Bad spark plugs: Spark plugs are responsible for igniting the fuel in your engine. If the spark plugs are bad, they will not be able to ignite the fuel properly, which can lead to a variety of problems, including cutting and idling high. Low compression: Low compression can also cause a variety of problems, including cutting and idling high. Compression is the force that pushes the piston down in the cylinder, which is necessary for the engine to run properly. If the compression is low, it will be harder for the pistons to move, which can lead to a variety of problems, including cutting and idling high. Clogged injectors: Fuel injectors deliver fuel to the engine in a fine mist. If the injectors are clogged, they will not be able to deliver the fuel properly, which can lead to a variety of problems, including cutting and idling high. Mass air flow sensor: The mass air flow sensor measures the amount of air entering the engine. If the mass air flow sensor is faulty, it can provide the wrong information to the engine's computer, which can lead to a variety of problems, including cutting and idling high. Throttle body: The throttle body controls the amount of air that enters the engine. If the throttle body is dirty or malfunctioning, it can restrict the flow of air to the engine, which can lead to a variety of problems, including cutting and idling high. If you are experiencing these symptoms, it is important to have your vehicle diagnosed by a qualified mechanic to determine the root cause of the problem. Once the cause of the problem has been identified, the mechanic can recommend the necessary repairs. Here are some tips to help prevent these problems from happening in the future: Change your fuel filter according to the manufacturer's recommendations. Change your spark plugs according to the manufacturer's recommendations. Keep your engine clean and well-maintained. Avoid running your vehicle on low fuel. If you notice any problems with your vehicle's performance, have it checked out by a qualified mechanic as soon as possible.

Check the timing. Sounds like its off.

that is your idle air control valve. it is located on the throttle body next to the throttle position sensor

just do induction / throttle body cleaning - will solve high idle on start up

Vacuum leak

check your TPS sensor
throttle position sensor

all engines have a rev limiter in them to keep from revving the engine too high,they all cut out about 1900 to 2000rpms.

2 airflow sensor out of operating range 3 coolant temp sensor out of operating range 4 oxy sensor indicates full rich 5 throttle potentiometer/airflow sensor... (low throttle pot signal with high airflow sensor signal) 6 throttle pot/airflow sensor...... (high throttle pot signal with low airflow sensor signal) 7 throttle pot...idle fuel adjustment failure(idle speed??) 8 intake air temp sensor...open or shorted circuit to sensor 11 Throttle pot at idle: Throttle pot idle trim out of normal range 12 Airflow meter: MAF signal out of range 14 Coolant thermistor: Resistance out of range or static during engine warm up 16 Air thermistor: Resistance out of range 17 Throttle pot: Out of range 18 Throttle pot/Airflow: Low throttle pot signal at high airflow 19 Throttle pot/Airflow: High throttle pot signal at low airflow 22 Fuel pump drive: ECU output to fuel pump relay 23 Fuel supply: Engine running too rich 24 Ignition Drive: ECU output to ignition Amp 26 Air leak: Engine running too lean 29 ECU self check 33 Injector Drive: ECU output to injectors 34 Injector: Looks for Injector dribble 37 EGR Drive: ECU output to EGR switching valve 39 EGR check sensor: EGR not working (normally pipe blocked) 44 Lambda (O2) sensor: Poor mixture control rich or weak (or misfire) 46 Idle speed Control valve: ECU output to Coil AB 47 Idle speed Control valve: ECU output to Coil CD 48 Idle Speed Control Valve: Stepper motor grossly out of position 66 Air pump: ECU output to air pump relay 68 Road speed sensor: Seen speed < 5km/h at high engine airflow 69 Drive/Neutral switch: Seen cranking in "D" or high airflow in "N" 89 Purge Valve drive: ECU output to purge valve
this is all I could find

check automatic idle speed motor if equipped.

yes, this is the case of a failed throttle body, in which case it needs replaced, the car is getting too much fuel causing the high idle. this needs replaced asap. you could proably find a small independant honda shop that could do the work for less.