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With a proper sponge filter and a heater I don't see why not, though a 5gallon bucket is a lot taller than it is wide so that might be less than ideal. Why not try something like a slightly larger rubbermaid container?
you can buy a cheap 10 gallon tank with a light hood and a HOB filter from wal-mart for about 19.99. My girlfriend bought one for her goldfish. Its not a great system by any stretch, but It would make an excellent QT tank!
I would spring for the 10 gal. set-up from wal-mart. A 5 gal. bucket will work, but does not have a lot of surface area to gas exchange. Plus, it is very hard to observe your fish in a bucket. Using a tank you can keep and eye on behavior and signs of infection like ick and velvet.
edit: the 19.99 ten gallon tank setup is acually 29.99. Still an excellent buy! and if anyone is serious about fishkeeping, they need a nice dedicated QT tank.