You need at least a 15gal container to attempt to grow an indeterminate tomato in a container. A 5 gallon is just asking for trouble. You can keep up production by starting determinate seeds at 4 week intervals so you have new plants coming into production when the old ones start to fade. You will probably want 2-3 5gal containers of these. They grow well here and they are big enough that one tomato sliced is perfect for one sandwich. The larger slicer tomatoes are too big imo unless you are making a lot of sandwiches because you have to store the remainder in the fridge.
patio f hybrid

I'm going to be starting my tomato seeds in a week so that they are ready to be transplanted out in the spring.

Also, if you want to cook, you really want a paste type. The slicers work,but are much too watery and need to be really cooked down to get a nice consistency in the sauce. Or if you take the seed goop out you get nice flesh, but the yeild is lower than a paste. oxhearts are an exception. They have a very high flesh to seed ratio.

A determinant tomato that might work for you is a bush version of Early Girl. It produces a lot of baseball to softball size tomatoes over six to eight weeks, is pretty disease resistant and doesn't need as much room as many other varieties. But, I agree that a larger pot (10 gallons or more) will give you a much better experience with any tomato except maybe a dwarf type.

You might want to ask this question on the growing tomatoes forum. There are a lot of container growers there, as well as several regulars who grow tomatoes in your area. For sauce as well as eating raw, many growers actually prefer regular tomatoes over paste types, which often get blossom end rot in smaller pots.

Here is a link that might be useful: Growing Tomatoes forum

lol, my paste tomatoes get BER if I don't put them in containers.