There is a small difference between intro texts in TOS:
Space: the final frontier. These are the voyages of the starship Enterprise. Its five-year mission: to explore strange new worlds, to seek out new life and new civilizations, to boldly go where no man has gone before.
and in TNG:
Space: the final frontier. These are the voyages of the starship Enterprise. Its continuing mission: to explore strange new worlds, to seek out new life and new civilizations, to boldly go where no one has gone before.
(emphasis mine)
It's pretty obvious that no man was changed to no one to include women. But, is there any explanation why was five-year changed to continuing? Also, why was it a five-year mission at all?
My only assumptions are:
Gene Roddenberry hoped to get funding to run the show for 5 seasons.
Gene Roddenberry just made up a number without any special meaning.
Gene Roddenberry was a communist.
Is there any official explanation, in universe or not?