Why does car stall after running for about 5 minutes

Sounds like a problem with air flow - like something is preventing proper air flow into the engine when it needs it. When the engine is cold, it benefits from less air flow, but when at operating temperature you need proper air, fuel and spark to operate properly. Ultimately, testing is required to find out what is happening here.

This could be a few things like a possible crank sensor that when heated created an open circuit. It can also be a fuel pump issue. You will at least need to start with a fuel pressure test while driving to see if it's losing pressure. Also scanning the car for codes can point you in the right direction. Alex