(covers information from several alternate timelines)
"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."
- - James T. Kirk, opening narration to Star Trek: The Original Series.
In the alternate reality, nearly a year after stardate 2259.55, the USS Enterprise, under the command of Captain James T. Kirk, began the first five-year mission of deep space exploration into uncharted space that had ever been attempted by any starship. (Star Trek Into Darkness)
The 2265-2270 five-year mission of the USS Enterprise mission was chronicled in Star Trek: The Original Series and Star Trek: The Animated Series, based on the opening narration to those series. The Star Trek Encyclopedia and Star Trek Chronology have conjectured that Captain Robert April had one five-year mission and Captain Christopher Pike had two five-year missions with the Enterprise before Kirk assumed command. These sources also state that Kirk had a second five-year mission after Star Trek: The Motion Picture.
Until 2259 in the alternate reality seen in Star Trek and Star Trek Into Darkness, a five-year mission of deep space exploration was unprecedented. Because the alternate reality was a divergent timeline that split from the original universe in 2233, there presumably had not been any official five-year missions prior to, at least, that year in the prime reality.
No references have been made to five-year missions after the 23rd century. Instead, the opening narration of Star Trek: The Next Generation refers to the Enterprise's "continuing mission". However, in 2363, the USS Olympia embarked on a similary-named eight-year mission. In an interview in the DS9 Season 3 DVD, Ira Steven Behr said that the USS Defiant was "on a five-year mission to kick ass."