Car dies after 5 or 6 miles

Start by having the error codes read and see if anything has faulted in the air, spark, or fuel systems. If no codes show, you can start with any of the three systems so your idea of it being the fuel filter or pump is as good as any other. If that doesn't fix it, go to the electrical side and check that you are getting spark (pull a plug and while it remains connected to the spark plug wire, crank the engine with the tip of the plug touching the engine block and observe if a spark is being generated). If you are getting a spark, then move to airflow. Insure your air filter is clean and flowing sufficient air. After that, you are down to checking sensors that manipulate the three systems. Good luck and be patient.