If you only swapped the tires and not the OEM rims, the TPMS light should not have come on at all (if the shop inflated your tires to the recommended PSI as shown on the placard in the door jamb). If you got new rims as well, you'd need to install a second set of sensors on the new wheels in order for the TPMS function to work.
When you start the car, does the TPMS warning light flash, or is it just a solid light? If it flashes upon startup, that indicates a malfunction in the system (usually a damaged or defective sensor in the tire).
First, check your tires to make sure they're at the correct PSI (or 1-3 PSI above, depending on personal preference). According to the 2017 CX-5 Owner's Manual, your car uses direct TPMS, which means that you have individual sensors installed on the wheels, inside the tires. You never need to reset these, which is why there is no TPMS Reset button on the dash. If you were to install new sensors, you would need to turn the car off and keep it off for 15 mins, then start it up and drive it for about 10 minutes to register the new sensors to the car.
If you're still getting the TPMS warning light, take it to a Mazda dealership. It's possible that one of the sensors is defective or was damaged during the tire installation. Mazda does sell new TPMS sensors, but I would suggest looking for aftermarket sensors instead. I bought a second set of 4 sensors for my CX-9's summer wheels. I paid about $80 I think, while a single sensor from Mazda would have cost me about $70.