I have seen peppers grow well in 5-gallon buckets and I have seen tomatoes as well.

Peppers, yes....but for most types of tomato, 5-gallons will be quite tight.

Josh

Greenman is right -- stick to the dwarf, grape and small cherry types if you do go 5 gal. Be aware that even many indet cherry plants (despite the small size of the fruit) can get 6 or 7 ft high and need a root system to support that. Bigger is nearly always better for tomato pots.

Last year I grew all kinds of peppers in five gallon buckets. I was amazed at how well they did, Just make sure you only put one plant per container. I also did some tomatoes in five gallon buckets and they did not do well. Even a couple of tomatoes I had in 12 gallon containers did not do as well as I had expected.

It depend on the varieties.
You can grow some peppers in 2.5, 3.0 gallon soil. Most should be fine if 5 gal. Smaller the pot, higher the frequency of watering and fertilizing.
Tomatoes, also if they are smaller DETERMINANT and bush type varieties can be grown in 5 gal. container fine. Probably they won't grow as big as if they were planted in the garden. I have seen right here (GW, thread) members grow them in 5 gal buckets. But I have also read that 8-12 gal. is more of a norm.