I'm replacing a Honeywell 5 wire thermostat with a Hunter 44600. The problem is the wiring is confusing. I have conventional single stage heat no heat pump. The wires on the old Honeywell are Red, White, Green, Yellow and Brown. The Hunter setup has a RH and RC jumper. I think the red wire goes into the RH (heat) but how does it cool unless you leave the jumper on. What is the brown wire for and where do hook it into the new thermostat?

Yes the jumper staYS ON RH AND RC.
Now as for the brown it is probably a common,, that goes to the c post, Hunter is so cheap and junky they might not have a c post
I`ve never ran into anyone that wanted to trade a good honeywell tstat for a hunter ,but oh well
You need to go to other end in the furnace and trace out what the brown wire is tagged to on that end,, what was it hooked to in the honeywell?

I figured it out. I'm going to get a Honeywell instead of the Hunter, Thanks for answering my question.

Smart man