I turn the forced warm air rheem gas fired furnace on at the thermostadt from off to hest and the furnace goes through its cycle and starts. It runs for 5-10 minutes and provides heat and then shuts off and does not restart itself automatically/ I can turn it to off and to het on the thermostdat and it will restart again. It has a vent pipe instead of a flue and it is windy and cold on the outside where the furnace vent pipe is located. Any thoughts?

Check vent pipe outside to see if its frozen shut(or restricted at all). Do you see any lights blinking in through the covers of the furnace when furnace is not working?

My furnace turn on for a few min and the turn off but the fan continues to run and blow cold air

You should have a flashing code on the control board that you can read looking through the small window on the lower blower door. Count the blinks of the light and it will give you the fault code. Are your return air filters clean?