Tyre manufacturers mark the sidewall of their tyres with the date of manufacture. You will usually find an oval with 4 digits indicating when the tyre was manufactured. The first two digits are the week in which it was manufactured the next two the year of manufacture. In the below image the tyre is marked 0907 indicates production in week 9 of 2007. A tyre manufactured in the 5th week of 2019 would read 0519.
As a general guide, tyre manufacturers warrant their product against manufacturing defect for a period of up to 5 years. This may not be true of all manufacturers and it is worthwhile checking to see what the warranty period is for the tyres you may intend purchasing.