I have been looking at the books, and now that I think of it command at 5th level is not out of the question.
Think about it, the Minbari are the most advanced race out there with the best trained fleet there is among the younger races, yet a Minbari can qualify for and take the Alyt PrC as early as sixth level, achieving the rank of Alyt-el and command of a support shiplike a Tinashi, Tigara, or Torotha.
Next we can look at the Centauri, who are also more advanced than any of the younger races save the Minbari. By taking the Noble feat at first level, a Centauri Officer (fleet) could perform great service to the Empire and take the Ascension feat at third level, gaining command of a ship of the fleet a a reward.
Therefore if a Minbari can command a ship at 6th level, and a Centauri at 3rd, why nota human at fifth?