During the 23rd century, Starfleet sent starships on five-year missions for exploratory purposes.
In 2269, Captain Kirk established to Odona that the USS Enterprise carried on board enough food to feed a crew of 430 for five years. (TOS: "The Mark of Gideon")
One of the greatest chapters in Starfleet history was the five-year mission of the USS Enterprise from 2265-2270 under Captain Kirk. (VOY: "Q2")
In an alternate reality, the USS Enterprise began its five-year mission under Captain Kirk in 2260. (Star Trek Into Darkness)
Background Information
The Star Trek Encyclopedia and Star Trek Chronology conjectured that Captain Robert April had one five-year mission and Captain Christopher Pike had two five-year missions. These sources also state that Kirk had a second five-year mission after Star Trek: The Motion Picture.
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 says that, in Star Trek: Deep Space Nine, the USS Defiant was "on a five-year mission to kick ass."