Answer: Unfortunately, a five gallon bucket is a bit small for most fruits with the possible exception of strawberries. You could try the alpines or an everbearing or day neutral type for an extended harvest.
Vegetables to consider would be tomatoes, peppers, bush varieties of squash, cucumbers on a trellis, greens such as lettuce and spinach, carrots, radishes, and so on. When selecting potentially larger plants, look for varieties labeled or described as "compact" or similar terms.
Many herbs would do well in such a container as well.
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