"Expiry" is a fairly vague term. It depends on usage, load, inflation, speeds of use, punctures, oxidation, hardening due to heat cycling etc. etc.
If you use a tire well within its rated load and speed, with porper inflation, on a suitable vehicle in good alignment, you can use a tire until the tread wears down to the tread wear indicators.
Having said that, typically, tires are designed to last about 5 to 7 years after production.