A man was born during a year in which the Johnson comet was visible in the sky. The next time that the comet was visible after man's birth year was in 2005. in what year was the man born?

We can see in the table that the Johnson comet is visible once in each period of 7 years.
So if the comet was visible in 2005, the previous year that the comet was visible is 7 years before, that is:
2005 - 7 = 1998
So the man was born in 1998.