None of this makes any sense to me. The OP expresses concern that chili spoils quickly (?) and that the hygiene of her campmates is bad. So the response to this situation is to make something like 40 16-oz servings of chili and eat it over three days, perhaps by keeping it simmering continuously. But maybe by splitting it into smaller containers and putting it into a cooler and reheating it. The OP seems to feel that if nothing special is done to it, the chili will be contaminated by the end of the evening on which it is first cooked.
How many people are going to be eating this, for how many meals a day? It would take eight people eating a quart a day each to make 5 gallons last only 2 1/2 days.
Boiling 5 gallons of chili, eating two gallons, then splitting 3 gallons into smaller containers and putting them in ‘coolers’ will not result in the 3 gallons cooling down to safe levels unless you have a lot of coolers with a lot of ice. A gallon of hot chili in a cooler just turns it into an incubator. It would make more sense to keep it simmering the whole time.
But then again, it would make a hell of a lot more sense to just make a fresh gallon (or whatever) of chili every day. Ingredients could be frozen ahead of time and thawed at the time of cooking. Tastewise, whether the ingredients are fresh or frozen at the time of cooking is kind of moot when the alternative is something that has been boiling for three days.
If hygiene is really so bad, it won’t matter how fresh the food is because casual contact between campers, handling common camp items, aerosol droplets, etc., will spread illness anyway.
I can’t reconcile the OPs fear of food contamination with the desire to prepare and keep food in a way that maximizes the opportunity for said contamination. Nor do I see why it would make sense to make more food than can be eaten in one day - maybe it saves some prep work initially, but now someone has to sit around and stir the chili pot and mind the fire continuously for the next two days. Where’s the labor savings in that? If you’re willing to leave the chili alone over an untended fire for hours at a time, how do you know that it was simmering the whole time, vs. burning or cooling off? Or that the fire won’t go out/escape? I just don’t see the upside…