Final answer:
The man was born in 1967.
Step-by-step explanation:
The Johnson comet, also known as Comet Halley, has a periodic orbit around the Sun, appearing every 74 to 79 years. The last time the comet was visible before 2005 was in 1986. We can calculate when the man was born by subtracting the comet's periodic orbit from 2005.
2005 - (1986 - x) = 0
Simplifying the equation, we get:
x = 2005 - 1986 = 19
So, the man was born 19 years before the last appearance of the Johnson comet, which was in 1967.