Up close, Egyptian goose with hatchlings
Well, of course Mike is right, the Sigma 500/4.5 should enable you to get closer and fill more of the frame, than my last post showed. I'm not at all experienced as a birder, I do know a fair bit about them, but in the past I always gave up on trying to photograph them.
Here in western Europe they are quite shy, and they have a keen awareness of their surroundings. I've only recently, after my switch to Pentax, picked it up again with the Sigma 500/4.5, when I found a used copy by accident. Whatever it is, that either makes birds flee when they are aware of your presence, ór tolerate you, I don't know. I dó know that birds tolerate people passing casually by with no real intention far more, than someone who stops in his pace, and points a large lens in their direction!
However, it is all part of the challenge, and practicing on a none-domestic goose is a nice compromise (because of course you don't want to photograph the ducks in the pond with a lens like the Sigma 500!)
So here (quite) a bit closer, and still without the 1.4tc!