Honeywell is my old thermostatand r,y,w wires were connected.my new thermostat is a hunter and the terminals are g,w,y,rh,and rc.
My question is weree I supost to conect wire r.

Jump Rh RC and connect to the R thermostat wire.

RH and RC are for the RC=Cooling and RH=Heating. When you only have one transformer in your system you jump the two together then attach the old R thermostat wire to the two of them. NOTE:It seems your system is not of standard wiring since the Green is not shown. The green is for the fan operation so they must be using relays to accomplish the fan operation in the cooling mode.

Since you did not post what type or model equipment you have this info is my best guess.