Since yours will be confined to a run, there are no rules, just personal preferences and the way we individually do things. Yours can’t just wander away. If they totally free ranged, yes, things would be different.
At 5 months they should already be roosting. I think that will help you, especially if there is no place for them to roost in the run, though they may want to roost on top of the coop. I don’t know if you have an elevated coop or if it is on the ground. I don’t know if you use a ramp if it is elevated. My grow-out coop is elevated but instead of a ramp I have intermediate steps. They usually don’t use the steps anyway, just fly up or down even at 5 weeks when I usually move mine. There are lots of different ways your coop could look. At five months I don’t think it matters that much. The way I understand it these will be your only chickens so you don’t have any integration issues. If you had older chickens already in the coop/run, that would make a difference. I just don’t think you are going to have that many problems.
I don’t know how well ventilated your coop is or if it is in the shade, but in Illinois this time of year heat is a danger. In cooler times I’d agree to leave them locked in there for a bit, but this time of year and not knowing what your coop looks like I’d say do not. If you get them late in the day so it has already cooled down (or if it is a rainy cool day) I’d say lock them up overnight and let them out the next morning. Otherwise just put them in the run when you get home.
They will go to sleep somewhere. If it is in the coop, good. If it is in the run and it gets dark down there, they will be very easy to catch after dark. Just lock them in the coop overnight. If you have a lot of light down there it may be more challenging to catch them. You do need to get them in the coop to sleep. At five months and with them almost certainly already roosting, I don’t think you will have to put them in the coop many nights for them to get the message. With my 5-week-olds and them not roosting it usually takes about a week for them to get the message but I have had some hard-headed ones take as long as three weeks. Each group is different. Each chicken can be different. We all do these things differently. There isn’t a right way or a wrong way, just different ways to get it done.
Welcome to the adventure. You are going to have a fun time.