i have attached a photo that shows the wires connecting the wall plate to the thermostat. does my wall plate have a terminal for me to connect a wire for ac power to the thermostat? right now my thermostat is not connected with ac power and runs only on battery. this is inconvenient because i have to change it every 6 months. this installation was done by a professional. i'd appreciate your help. thanks!

I agree, you need the "c" wire, the "R" is one side of the 24V but the "c" is needed to complete the current. Look at the stat wire behind the baseplate shown on your pic to see if there is another wire in the bundles you can attach to the furnace and then to this baseplate. If not, pull a new wire behind the existing, if its not nailed down in the wall or go to home depot and find the type of stat we call in the industry as "power robbing". It is made to replace stats with 5 wires like yours but does not need the "c" terminal. It robs power from "R" to "W" or "Y". Anyway, this will at least get you out of the battery replacement and avoid pullling the new wire if its too hard.