Well, I'm going to go against everything everyone here has said.
Reasons? She's five. Obviously small. And already shoots, from a bench, I would guess, a 10/22.
Since she's five, her shooting a 20ga would likely be 5-7 or more years away. Her ability to shoulder, hold up, and swing a 20ga is a long time coming.
Get her a BB gun. Knock off the sights, and have her shoot instinctively at stationary targets. Get her comfortable now with shouldering and shooting freely away from a bench. When she gets good with the stationary shooting, move to a big ball of aluminum foil. Rolled or thrown straight away underhanded will allow her to start out slowly. It will absorb the hits and you can look at where you/she hits.
When she develops the muscles and coordination of the swing shooting, depending on her progress and accuracy, you very well COULD go to a .410 for straight away targets from a ground thrower. And if I remember right Casey, you shoot from your own land and use a home thrower? Right?
You can have her shooting a shotgun, like a Stevens 311 .410 or a CZ/Huglu .410 O/U or a SxS in just a few years versus several years with the larger/heavier guns.
To start solely with a .410 on moving targets (skeet, S/C, trap - at ranges) is a hardship on a young shooter. If you do it with consideration on developing the shooter, you'll have a marksman(woman) on your hands that'll outshoot you and everyone around.
Whatever you do, take your time and be very patient, as I can tell you already are with your daughter. My daughters are now 19 and 17. The older one used to shoot a few years ago, but even at 5'6" and 17, the 20 was still a bit much for her to hold up and shoot accurately.
Don't rule out the .410.....and a reloader :wink: