Late to the party but my '05 5.0L GXI did that. Took it in and marina did a tuneup on it - plugs, wires, cap, etc. Problem was fixed.
If you haven't done those parts yet, I'd look into it.
Low fuel pressure on my '05 caused a high pitched whine that was very cyclic. You couldn't keep the engine running, constantly having to restart it. That was a $1k (installed) repair bill as the fuel pump was NOT rebuildable.