Tires...how long do they last???

The radial tires on my '66 Form. S are at least 9 years old and show no real wear or aging. Sidewalls look great (no signs of weathering or cracking), treadwear is perfect & traction is fine! Based just on its age is it time for a new set? A tire place told me that tires, regardless of treadwear should be replaced every 5 years.

ZOOKYPR