Cats are crepuscular animals. They are "programed" do start at 5 AM, hunt, and go back to sleep until afternoon. Living in homes tweaked them a little, but the 5 AM thing is still strong in a lot of them (mine included).
https://www.animalhumanesociety.org/resource/cat-keeping-you...
> You are unable to access animalhumanesociety.org
Is this because I laughed when our family dog fell down the stairs when I was six years old?
So not specifically at 5AM, but around twilight. In my area, and for my cats, that changes a lot between summer and winter.
Same for my chickens, which is why "automatic chicken doors" are difficult/impossible around here: It'd need to calculate sunset and sundown, and then also consider clouds and trees: in winter the sun sets around 16:30, but the low angle makes sunlight more blocked by clouds, particles and trees and such. My chickens often decide its bedtime before 16:00 already.
It worked most of the times, until in winter, twice, some chickens were locked out. First time I saw it in time. Second time I only found feathers the next morning and one chicken less in the coop.
While on an especially cloudy (snowy) evenings, the door would be open when it was almost pitch dark out there and I caught a fox near already.
"The Real World" is just messier than a mathematical representation can be. I use https://sunclock.net/ and have built a watchface like that for my fitbit like that. The mathematical model is perfect as guidance. But it's not reliable enough to bet the lives of my chickens on it.
Your best bet, if you really want an automatic chicken door, is to get a dumb one that just opens when powered on and closes (via springs) when powered off, then plug it into a smart outlet automated to turn on at sunrise and off at sunset.
Most commercial automated doors work on solar + a battery.
I made mine to open at actual sunrise (except in the summer; I keep them in until 7am because the coop is cooler, and if let out they can get loud before my neighbors wake up) and close it at actual sunset (not civil twilight, which most people think of when you say "sunset"). Generally the door is open well after the birds are in bed, which is fine.
Aside from some dumb birds when they were younger, I've never had one locked out (and those dumb ones were trying to nest in silly places, and weren't going you come in no matter when I closed the door).