Would you wait until you had 5, 1-gallon batches in the fermenter before you pitched your yeast?
If so, I foresee a problem if any bacteria should find its way into the fermenter. The sugars may be (in part), already consumed by bacteria by the time you finally pitch your yeast, and thus, you'll have competing cultures. Also, you'd risk oxidation.
If you pitch your yeast after 1 1-gallon brew, then just continually add wort, I would be concerned about the under pitching your yeast.
You would have to re-pitch yeast everytime you add more wort, but with the reproduction of yeast cells in the wort already, you would have to account for the number of daughter cells to gain an accurate amount of how much yeast you'd have to pitch every time.
Honestly though, I have no experience in this matter. These are just my .02 on possible outcomes. I would love to hear a Mod's opinion.