I have a goodman furnace model gcs90904cxa. All filters are brand new blower replaced last year new limit switch vents open in house exhaust and incoming air vents clean inducer motor free turning. Replaced flame sensor and thermostat everything starts up normal as it should no problems starting runs for about minutes then burners shut off and 4 beeps for high limit switch fan runs for about 3 minutes and it starts the cycle all over again every 5 minutes after that. Cannot find any air restriction. Also removed blower and cleaned top of secondary heat exchanger Was alot of dust build up. Am at a loss trying to figure out what is causing the high temps could the main heat exchanger be causing it or maybe an inducer motor is slowing down as it heats up had to replace that about 5 years ago?
You should not have a big buildup of dust if all filters are in place. Is a filter missing? Your furnace manual says that some internal filters are not included. In any case, dust may be restricting airflow.
Why was the high limit replaced? The replacement may not be proper spec or it could be defective or could have failed early in its life. Suggest you measure the air temperature in the main duct to see if the high limit is tripping too soon. If you don't have a thermocouple probe, you can drill a small hole in the main duct and insert a meat thermometer. Repair hole with aluminum tape or caulking.
When the blower was replaced, did the tech set the correct blower speed to achieve the desired temperature rise? Perhaps not. If the blower is running too slowly to remove heat from the heat exchanger -- perhaps due to dust buildup -- you will exceed high limit.
This is the procedure in your manual: