5 seconds of idling, then died? Thats like it depressurized...Like you spun the pump up, but it won't stay 'on'...
have you messed with anything on top of the sending unit under the rear seat? Pull the plug, and use a multimeter to test that...I don't know the numbers off the top of my head, but you'll need to check it with the key on, ready to start, and under cranking from what i remember (so you'll need a friend for that)...I had a built NA engine in years ago, and did a temp install with a motec. I ran a separate line inside the car, under the rear seat cushions, to the sending unti/pump housing from the new computer, and for a while had exactly what you might have...could get the pump to spin up enough pressure to start, but the pump was not running after cranking...and then would simply idle until the lines were clean.
I had no luck with 'listening' to the fuel pump. Not positive how the stock ECU does it, but the motec's default start settings that i had borrowed would not start the pump until the engine was physically cranking...some cars will power up the pump before cranking, some don't. listening to the pump when the engine was on, with nearly 13:1 compression, full AWR mounts, and a completely cold engine idling at 1400 rpm...I couldn't hear anything in side the car, let alone the whirling haha. We fixed it by adjustments to the motec's cold start cycle, by having it always on with the key on (not ideal, but again...this was temporary anyway) so i'm sorry...don't really know what to do for yours, but see what readings you get out of that harness plug with a multi-meter on and off cranking...
that will rule out if its still your relays up front, anyway...it could simply be a dead or dying fuel pump...
