Re: How common are five year missions?
It has to depend on assignment. Some ships would have routine patrol duties along regular spacelanes between systems in Federation territory, say between Sol and Rigel. It seems unlikely a ship would be doing that constantly for five years before getting a new mission.
And now I see Christopher
has already covered that.
Dr. Howard, Dr. Fine, Dr. Howard: For duty and humanity! --Men in Black (1934)