Ok, I've heard this a couple of times and I gotta ask. 2014 SD 6.2L gas with the key just inserted into the ignition switch (not turned either direction), I hear a high pitched hum/vibration coming from somewhere under/near the engine. Almost sounds like a fuel pump running dry. Again, not the fuel pump as I cam hear it if I rotate the key.
Maybe a relay coil? Sounds for 3 to 4 minutes and stops and doesn't do it every time.
Its not the fuel pump. I have wondered about this noise as well. First of all, its coming from under the hood! Plus, the fuel pump prime only runs for a few seconds, not 5 minutes. It usually happens to me if I put the key on to the first position (ignition off) so I can run the radio with the doors open. There is a high-pitched but quiet hum coming from under the hood, maybe on the driver's side. It will last for 5 minutes or so, maybe more. I haven't really, really tried to figure it out, but it baffles me. These trucks are not diesel, so I doubt they have a vacuum pump for brakes. I'm just surprised whatever is running needs to run when the ignition position is not selected.