Born June 5, 1723, Kirkcaldy, Scotland: Died Edinburgh July 17, 1790, age 67.
Of course few things are quite that simple. June 5 was the date his baptism was recorded at Kirkcaldy church, so his actual birthday was almost surely a bit earlier; but custom and tradition have marked it as June 5. Second, in 1752 Scotland converted from the Julian to the Gregorian calendar (Catholic countries had done so in 1582 but Protestant countries including England and Wales, Scotland, and Ireland, as well as the colonies, took longer to make up their minds). So June 5, 1723 (Julian) became June 16, 1723 (Gregorian).
We’re sticking with the traditional date under the calendar in effect at the time, so there you have it.
Happy 295th Birthday, Adam Smith!