Dunno what year of car you are driving but it’s highly unlikely you did any damage to your car. If it was only 5-10 minutes then you’re most certainly fine as long as you are up to date on your oil changes and you weren’t low on oil.

You’re thinking of DRLs, which all new cars sold in Canada after a certain year have.

You might just want to avoid buying a car with telematics or an LTE connection then. Chevy and Subaru should be off your list too. Probably others.