Why does my 02 Pontiac Grand Prix stay running but dies after driving it for five minutes after changing the fuel pump

First you need to determine if it is a fuel problem or electrical problem. Using a fuel pressure tester will help. Secure it to your windshield so that someone can watch it and when it does take note of the pressure, You can also run a noid tester to see if the injectors are loosing current and a spark plug tester. Simple second, hook up a scanner and see what codes are present and what information you get when the engine dies.