Scott this sounds like a bad safety control unit, you can test the Photo Cell to make sure that is not the problem by running a jumper wire between where the White and Blue wire connect although I don't think that is the problem because the unit is running fine for 5 minutes and you are also getting a reading from the photo cell, but I would still try this first.
If the unit still shuts downs after 5 minutes you can wire the safety control and photo cell out of the system "JUST TO TEST" the unit and see if it will then run.
Take both the safety control and photo cell out of the system and then connect the Black wire from the power cord to the Red wires from the Igniter, Motor and Motor Relay together.
Then connect the White from power cord to the motor and Igniter lead.
You should now be able to run the unit in a "TEST" mode to see if this takes care of the unit shutting down in 5 minutes.
If this solves the problem then replace the PP203 Safety Control.
You can order the part at http://www.allpartsinc.com/ProductDesc.aspx?code=pp203