Answer: Watering problems are often related to the soil mix you use as well as your watering routine.
A five gallon bucket is adequate for a full grown tomato plant as long as you are careful with the watering in late summer when the plants are large compared to the available space for roots and the weather also tends to be hot and dry. Early in the season (plants are small relative to soil volume, weather is cool, rainfall is frequent) you will not need to water as much or as often as you will later on. Also make sure your container has several drainage holes in the bottom so any excess (such as during a rain storm) can drain out easily.
The soil should be evenly moist yet well drained, meaning not sopping wet or saturated, your goal is damp like a wrung out sponge. To know if you need to water, dig into the soil with your finger and see. If it is still moist, do not water yet. When you do water, water thoroughly and slowly so it soaks into the soil.
Eor a container tomato I would suggest a good quality, brand name (usually these are more expensive) soil-less mix formulated for container plants. Sometimes these will also include a water holding polymer to help the soil hold water better (you may need to reduce watering accordingly, especially early in the season) and may also have some initial fertilizer.
I would also use some good quality compost or well composted manure as a top dressing periodically during the season along with a regular fertilization program. You could use a slow release form at planting time (read and follow the label instructions) as well as occasional foliar feeds using a water soluble fertilizer, again read and follow the label instructions. Look for a complete formula such as 10-10-10 plus minors.
There are many searchable gardening articles and a searchable Q&A archive at the web site for the National Gardening Assocation, look to the left under "Expert Advice".
You will also find very practical and straightforward information for new gardeners in the gardening books in the Dummies Series. Gardening for Dummies is a good one to start out with, then you can look into some of the more specialized books such as Annuals for Dummies or Container Gardening for Dummies based on your interests.
Your local county extension should also have publications available to help you with growing different kinds of plants in your local area. Gardening is often learned through trial and error, too. (grin)
Good luck with your tomatoes!
Q&A Library Searching Tips