Nothing like Speed Of Plot. During TOS, looking at how the episodes are spaced out, I think the Enterprise was never more than six months away from Earth, Vulcan, or the Neutral Zone. Assuming it even made it
that far.
"Balance of Terror" --> Early-ish in S1 --> The Neutral Zone
"Tomorrow Is Yesterday" --> Middle of S1 --> Earth
"Amok Time" --> Beginning of S2 --> Vulcan
"The Deadly Years" --> Middle of S2 --> The Neutral Zone
"Assignment: Earth" --> End of S2 --> Earth
"The Enterprise Incident" --> Early in S3 --> The Neutral Zone
So, yeah, the five-year mission of "to boldly go where no man has gone before" meant about as much in TOS as "to boldly go where no one has gone before" meant in TNG. It was just a slogan. They were always nearby.
And Earth in Star Trek must be close to one end of the galaxy if "Where No Man Has Gone Before" and "By Any Other Name" are anything to go by.
With Pike's five-year mission, other than "The Cage", I think the writers have a second chance to make a five-year mission go the way you'd think it would go in theory.