Question on Smart Thermostat Wiring

https://zukoski-group.chbe.illinois.edu/index/index.php/Getting_Your_AC_Ready_for_Summer_With_a_Comfort_Experts_Plan_to_Avoid_North_Fort_Worth_AC_Repair_Calls

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