1. If the light isn't changing much you can just use manual exposure mode for birds. Meter on some fixed object and dial up or down by as much as a stop if the bird is much lighter or darker than what you metered on.
2. The 400/5.6 is sharp wide open. Unless you're close enough to the bird that DOF becomes an issue that's the aperture you should shoot it at.
3. If you're tracking the bird on a loose gimbal head you can go to a somewhat slower shutter speed than pure handholding, but this depends on lots of factors (like how smooth you are in tracking). I wasn't great at this, but could usually get away with ~1/200s with the 400/5.6. (handholding without a tripod I wasn't happy with results below about 1/1000).
4. Don't be afraid to bump the ISO up. Yes noise is annoying, but it's a much more recoverable defect than motion blur or serious underexposure.
5. GET CLOSER. I know this isn't always possible, but nothing (not even focal length) compensates for being too far from your subject. All of my best bird shots are from less than 200 ft. - most from under 100 ft.
Anyway, Dave (dcstep) is a much more competent bird photographer than I am these days and maybe he'll have some even better pointers.