I get paid a flat rate too allowing me a max of 10 days vacation and 5 days sick per year. That said, in over 20 years, I have taken 2 days off sick. I do think actually taking the 5 days is a lot especially if you are also closing early sometimes. Bear in mind, we are self employed and not employees so it's going to annoy client's if you are acting like an employee and closing early or allocating yourself too much time off, especially if you are expecting them to pay for it.
I don't think it's reasonable to have it both ways - i.e. early closing at times and paid time off. If we are contracting for our service to be available between certain hours and if our contacts also allow us time off, then expecting client's to come early too some days is taking advantage.
At least if you have some paid days each year, you can then provide lots of notice if you won't be open on a given day and use that from your contracted paid days.
While I totally understand that you get sick sometimes, it isn't always the cost that parents struggle with. It's the reliability. They have to work which is why they arrange for care of their child. Closing early or short notice sends all the families into a scramble. They better understand if that's not a common occurrence.
To have had 3 sick days already this year and we are barely out of March would also have me concerned if I were one of your client's. At this rate, they are looking at one day a month - 12 days a year. That is a lot.

Why do you think you are getting sick so often? Are you sanitizing your toys regularly not just cleaning them? To santize toys they need to be in bleach and hot water or disinfectant and hot water for a prolonged amount of time. A quick wipe with a disinfectant cloth is not enough to kill lingering germs and the green cleaners or white vinegar solutions do not offer sanitizing.

Is the bathroom you are using for day care cleaned at least once a day? What about the bedding the children are on and their sleep mats? High chairs? Door knobs? Hard surfaces the children touch? Have you been checked for other underlying issues?

If I am frank - if you were my provider and closing early with 5 sick days last year and three already this year, I would be looking for a more reliable provider.