As it was said before the death of Kirk's son David (part of Star Trek III) happened 11 years before StarTrek VI, which took place 2295. In that year Sulu was Captain of the Excelsior for "more than 10 years". He left the USS Enterprise-A after one year of service to be the captain of the USS Excelsior (p. 19).

In StarTrek V. he served under Kirk. And we saw in that movie, that the Enterprise-A was not finished. After all we have to believe, that StarTrek II., III., IV. and V. follows in a direct line.

For Star Trek V. we could think about the year 2283 or much better 2284;
for StarTrek II. before that but still anything between 2282 and 2284.

References from StarTrek V.:

• Spock went to Starfleet 30 years ago. (p. 191)
  That line could again be read as "26 to 34 years ago"; therefore we are back sometimes (2283/84 - 26/34=) between 2249 and 2258.

TOS "Journey to Babel" is part of the second season TOS. That is the calender year 2266.

In this episode we learn that Spock and Sarek have not talked to each other as father and son for 18 years, because Spock chose Star Fleet service and did not attend the Vulcan Academy of Science.

So the event above must happen (2266 - 18=) sometimes between 2247 and 2248.

Spock could have joined StarFleet the same year or one year later - therefore sometimes between 2248 and 2249.

With the statement aboce from StarTrek V., we can be sure that it was in the year 2249! The quarrel between the two Vulcans must have happend 2248. And StarTrek V. must play 2283.

Spock says in "The Menagerie" that the Enterprise's visit to Talos IV happened "thirteen years ago". This episode was part of the first season of TOS, which plays in the year 2265.

Therefore the episode "The Cage" happened (2265-13=) 2251 or 2252 and we are in the time of Captain Pike.

Spock entered StarFleet-Academy 2249 and stood there between 3 and 5 years. So he graduated sometime between 2252 and 2254. But Spock was part of the Crew of Pike on Talos IV!

• Spock was brilliant and his graduation must had happened 2252.
• The Talosians are contacted in "The Cage" by the USS Enterprise under Captain Pike also 2252.
• 18 years earlier the S.S. Columbia disappeared; that must had happened 2233 or 2234.

Spock also says that he served with Pike for "eleven years, four months, five days". Maybe Spock served under an unknown commander for "x" years after he served with Pike and before he served with Kirk: Graduation + 11 years + 4months + 5days + x = The date, on which Kirk took over command!

Graduation + 11 years and a little bit + Time with Commander "x" = Begin of Kirk's mission = 2264
2252 + 11 + x = 2264
2263 + x = 2264

This "x" is a year or less. That does not sound like an other commander. It is more likely that there was a refit. That would give us a clue why the crew grows from 200 people under Captain Pike ("The Cage") to over 400 crew-members under Captain Kirk. Maybe Kirk was already Captain during this refit, because this time is not part of the 5 year mission and in this time he could learn everything about his new ship and crew. Captain Decker did the same 5 years later. But we can't be sure.

• Pike is promoted to Commodore in 2263 or 2264.

As mentioned before Admiral Morrow says in the third StarTrek-Movie, that the Enterprise was "twenty years old". There he takes reference to a radical reconfiguration. With the new technical equipment more people could serve on a starship.

We know, that Kirk's Enterprise is a ship of the Constitution Class. But very often something is said about an "Enterprise class" - and it is generally said that is an error. Maybe the original class of the starhips was called: "Enterprise-Class" in the times of April and Pike. Therefore the Enterprise would be the first ship with this special design. This could be true, because Kirk's ship is often said to be the first ship of the fleet (but other ships of the Constitution Class are commanded by higher officers).