My business has been closing at 5pm daily with $120 of marginal revenue and about $80 of marginal cost in the last hour open. What can I do to maximize profit for the day?

Reduce costs.

And/or increase sales.

You can't just isolate one hour of the day without figuring out what that MEANS.
I for one have rarely heard of a business that closes at 5 pm, when most customers are elsewhere, mostly clogging the highways and byways in their cars, possibly trying to get to your place. Off the top of my head, I would say stay open later. Often this means seeing what businesses around you do. Many small ones where I have lived all stayed open until 9 Thursday evenings. Those in the building/lumber/equipment trades, on the other hand, open early in the morning and close early. Your question is lacking a lot of info.