This page contains information regarding new Star Trek material, and thus may contain spoilers.
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.