1995 bmw 540i sputtering on startup. Fuel pump bad?

Here's a link to your fuel pump relay. BMW E39 Fuel pump relay locations Tech Bentley Publishers Support

It won't be pumping fuel if it's bad, remove pump and connect to battery you will feel vacume with your finger

broken wire between relay and pump

Go to google--enter 1999 bmw 540i obd2 code P0011

Hello---Sounds like your injectors are not firing. I doubt ALL of your injectors clogged or failed at once...Troubleshoot a lack of input signal to PCM from crank position sensor or cam position sensor, or bad PCM driver circuit. Injectors should usually have power when key is on. PCM grounds other side of injector circuit to pulse the injectors...
Fuse #23 will be the pump fuse, you should have 50 psi of pressure at the fuel rail.
I hope this helps.

if you have 12 volts at the pump and it doesn't run it's the pump.
If you have 12 volts at the pump it means the relay is doing its job and the fuse is ok

remove the pump and run 12v to it directly from the battery to test the pump.

I would check the fuel pressure just after starting and again after 10-15 minutes (or before it dies). Sounds like a fuel delivery problem. Could be a stuffed up filter, or the fuel pump could be dying. I had a Volkswagen some years ago and it had two fuel pumps, a large one up in the engine bay and a small "helper" in the gas tank. The one in the gas tank was bad but the bigone was fine, so I'd start the car normally, drive for about 20 minutes, then the car would die and not want to start again until it had cooled off. Maybe you have the same setup.

Check the fuses. If they are in good shape then the problem is the wires to the pump

look in the truck

You must check to see if you have power at the fuel pump relay which is probable in a fuse box under the hood.