I always felt that the "5-year mission" was really akin to a standard deployment, particularly for a Constitution-class starship. I think much of Kirk's monologue in the opening credits is much more for the benefit of current-day TV viewers to explain why the Enterprise is otherwise wandering out there every week, and need not necessarily be taken too literally within the context of the show itself. IMO, the Enterprise really seemed to be a multipurpose starship, with exploration being just one of the things she can do.