are you saying the fuel pump stops working?daft question but is there plenty fuel in it? how handy are you with electrics?? if yes then get a test light or voltmeter across the pump terminals to see if the feed or earth is dropping away after 3/5 min running. if yes you need to start looking in the direction of fuel pump relay/associated wiring or possibly ecu (ecu controls relay). you could hard wire the pump onto a battery as a test to make sure pump is ok and see if the car runs for more than 5 moin.