My old thermostat Total line Gold P274-0109-0150-0200-0300 had six wires, red, yellow, green, blue, white, yellow, and orange. The orange wire connects to another orange wire connected to the Air condition unit outside. (See attach doc)

But my new Honeywell RTH110B none programmable thermostat only gives instructions for wiring up to 5 wires. The connections are Rh Heating power supply, Rc Cooling power supply, W Heating signal, Y Cooling signal, G fan. How do I wire my new thermostat using the six wires previously used in my old thermostat?

You probably have a heat pump. The thermostat that you bought will not work on a heat pump. You need the reversing valve leed