Question on Smart Thermostat Wiring

https://telegra.ph/Booking-AC-Repair-in-North-Fort-Worth-With-Comfort-Experts-Step-by-Step-11-13

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