Question on Smart Thermostat Wiring

https://connersuhm791.clarionvale.com/posts/thermostat-checks-to-try-before-calling-comfort-experts-for-ac-repair-in-north-fort-worth

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