Question on Smart Thermostat Wiring

https://edgardgtw273.tearosediner.net/tripped-breakers-and-ac-repair-in-north-fort-worth-with-electrical-help-from-comfort-experts

Question on Smart Thermostat Wiring Our older thermostat only has four wires and no C wire. The smart model I bought says it needs one. Is an adapter safe to use, or does that cause problems with the AC down the road? Trying to avoid a wiring mistake