it is -5 degrees outside. Our thermostat is set at 70 degrees and the house heat is 58 degrees. the fan blade on the unit outside is not moving. the hvac system inside has a sticker on the unit. the empty box says unit has electric resistance. the checked box says 'may install' electric resistance. I see no mention of auxillary heat on the thermostat. Last summer hvac man was here and he said our thermostat is the correct one for the system. is everything ok and we just need an auxillary heat, or is something broken?
Heat pumps work by removing heat from the environment and exchanging it "elsewhere." In the summer, the heat is removed from the environment inside your house and ejected outside.
For the cold seasons, the air outside has heat removed from it and transferred to the inside of your house. This works great until temperatures reach 20-25° F, at which point, the efficiency drops below that of the equivalent elecrical consumption of a resistance heater.
It would appear, based on your description, that you are in need of that additional device for your system.
There is some variance regarding temperature balance, with lower figures attributed to higher performing, more efficient heat pumps.
Some information located here: Heat pump explanation
-5 (I assume °F) is a too low temperature for heat pump to work properly (usually those stops working at -15°C [+5°F]), so outer unit is simply 'locked due to excessive cold'. Auxiliary heat, in some units, is controlled directly by the HVAC controller and not by room T-STAT.
Anyway, check if auxiliary heat is connected BOTH on HVAC unit and Tstat, if it's connected only at unit side, connect it to the t-stat, if it's not connected, probably auxiliary heat is not present on your machine (if it was ECU controlled you won't have that cold in your house).
For now, you can just buy a couple of kerosene heaters and use those in case of emergency, look for 'zibro kamin' (I suggest a model that can work in case of power failure).