5 gallons is a good size because you will be able to move the plants easily. You don't want to set them out in the sun all day there in Az. Use the potting mix. It will retain moisture better than the soil. You might consider putting a plastic pipe down into the pail so that you can water from the bottom up. Put your drain holes in the pail at least 4 inchs up from the bottom so there is a space at the bottom that will act as a resivoir allowing the moisture to be drawn up as needed. Use plastic sheet to cover the surface to reduce moisture loss due to evaporation. When the plant gets larger, a vertical support may be needed, so might as well put it in when you set the small plant in the pail. Make sure that the potting mix is plenty moist when you start out. Add water to the pail through the fill tube (plastic pipe) until the water comes out of the drain holes that were placed up from the bottom about 4 inches. washed gravel or small rock would be great down in the bottom of the pail to form voids for the water resivoir. You can use a liquid plant food mixed into the water or make a strip of something like 10-10-10 on the surface under the plastic mulch cover away from the plant stalk. It will gradualy leach down into the potting mix to supply the fertilizer. Organic fertilizer would be best. Add a table spoon of epsom salts to the potting mix and if you have it, some bone meal. chuck

Here is a link that might be useful: A simple grower project

Chuck, thanks so much for posting!I visited your site earlier and saw your containers and bookmarked it. That was one of the very first things I did when I came to this website. Can you explain why you use the landscape cloth to suspend the soil instead of just planting the directly in the container?
Also what do you mean by 10-10-10? All the garden lingo is new to me, so sorry if I sound annoying. Potting soil and potting mix I thought was the same thing. I did do as you suggested and had my husband drilled holes 4 inches up the sides, put in some rocks from our landscaping and my daughter and I had fun planting the tomatoes. We also had to repot the "lone lima bean" that came home in a dixie cup, thats what started this whole learning project for us.
I am going to try your planters for an eggplant! We love those!
Thanks so much Chuck, you have opened my eyes to something that I think I can actually do in a container..because my ground here is caliche I could dig and dig then hit a boulder!

I'm growing several tomato plants in 15 gallon pots, one plant to one pot. I just fill the pot with straight potting soil, mix in Dr. Earth vegetable fertilizer according to the directions on the box, plant the tomato plant, add the tomato cage, and mulch with potting mix and mulch, 2-4 inches deep once the plant is larger. The larger pots don't dry out as fast as the five gallon size, in our hot, dry weather. The pots can be planted with cold weather vegetables over the winter, and re-planted with tomatoes again next year.
Below is a link to an article explaining fertilizer numbers. I used to mix up my own organic fertilizer, but with so many good ones on the market now, it's not necessary. Miracle Grow liquid tomato fertilizer is very good also.
Good luck with it. When I taught first grade, every spring my class would take some gardening project home.

Here is a link that might be useful: Understanding Fertilizer numbers

In Arizona your main concern is going to be SHADING the pots, especially if you are using plastic. I once moved my roses in pots onto my grass in the Sacramento summer for ONE DAY, and the grass underneath was all yellow from being fried. Imagine what's happening to the roots inside the pots! And I've also grown tomatoes in the Palm Springs area, and it's difficult this time of year because it gets too hot for them. But the plant part can do OK in the heat--the roots will not.
If I were you, I'd put the pots where they get morning sun only ('til about 11-12), with a small table or something like it in front so it throws a shadow on the pot as the sun moves across the sky (just shade the pot, not the plant in it) You could also wrap the pot with insulation or a water heater blanket to keep it cool. You also would want to mist the plants with the hose in late afternoon/evening to cool them down. When it gets over 100, the pollen suffers and it's difficult for the fruit to get pollinated, so when it gets hot here, I take a watercolor paintbrush and "paint" the flowers early in the morning to get them to make fruit. Even misting them and hand-pollinating them, you might not get very many fruit after the nights get in the over-90-degree range. But it will be a fun experiment for your daughter!
Have fun!

Carla in Sac

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shade the containers as best as ya can without shading the plant..

WOW! thanks everyone! I have been reading about pruning,I guess the early girl is an indeterminate plant and I have to snip off some suckers. I am wondering if I should remove all the leaves and stems below the flower line? the flowers are pretty close to the top. I saw one flower, closed on the other plant. Will the flower turn into fruit? because the early girls flowers are pointed downward and open and I dont see anything.

Astascosta_tx: I'll need to shield my pots too as it gets well over 100+ here in the summer. I like the foil board idea. I'll neded that as my deck gets so hot I can't walk on it with bare feet. NASTY HOT....I hate it too.

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teesaz: You have to wait till they pollinate until you see the baby fruit appear from the flower. Give the plant good shake during the warmest part of the day & you should be able to see the pollin drop out of the flowers. Only time will tell. Don't chop them down too much or the will get sun scald on the maters.