Let's say I ordered a package via usps priority mail on Wednesday April 23rd. It was shipped out Thursday April 24th that morning. It's coming from Oklahoma to Illinois. They told me I should receive it in 5 business days. However, usps runs Saturday at my post office and I didn't receive it then. That's where I'm confused at. Do I start the countdown from Wednesday or Thursday and also count Saturday? Which day should I get it?

I wouldn't expect it until April 30 (I wouldn't count the day I ordered it, or Saturday). If you get it soonner, great, but don't plan on it.

You don't count Saturday as a business day.

5 business days. You don't count Saturday or Sunday. Not sure WHY they gave you 5 business days; but that is what it is.

you start the countdown once the package has shipped so that would be Thursday. I'm not sure about counting Saturday.