Not that I've actually done it, but I would expect that fish can live for an extended period of time in a 5gal bucket. As long as you keep the temperature regulated and perhaps throw some bubbles in there (aka air pump) to keep the water moving (and oxygenating) it would be no different than keeping the fish in a 5gal tank for years.
I would recommend keeping the buckets in a dark room if possible as the dark will be less stressful to the fish, especially considering the moving circumstances which always stresses fish out.
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Cheers,
Andrew B.
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