what are the Labels (Letters) for the orange and yellow wires above the screws? Is the Orange "O/B" and the Yellow "Y" ?
The google store has a compatibility checker for the thermostat where you can match your wires (by the letters on top of the screws they are connected to) which should help. Look for the confirm compatibility hyperlink. Heat pumps usually have the orange wire connected to O/B. Your yellow wire looks like it might have a Y above the screw which should be for the A/C. There is a great video on you tube about wiring for a nest thermostat with a heat pump. If you do a search it will bring it up. Look to me like it can work for you.
If you go to the theroma=stat page it has a compatibility checker
