2013 mazda cx5 cold light not going off and poor heat
Offhand it sounds like a bad thermostat.
Get it diagnosed quickly. It is not a good idea to ignore this one.
Check coolant level in cold radiator and if full, replace thermostat,.
A concern here is that there’s coolant leak. That can cause severe engine damage. Early signs are consistent with low level of coolant: it’s too low to reach one or more temperature sensors, or the place on the engine where a hose connects to the heater core.