I want a box that will natively support an external hard drive without needing some sort of USB power hub. I tried looking that up here but I couldn't find much answers pointing me to specific boxes that would definitely support a hard drive of this size.
I'm thinking that you should start by figuring out how much power (current/amps) that your 5TB portable USB HDD needs.
Then check that against first the type of USB port that the various Android TV boxes you are looking at have, and then see if they list how much power they are able to provide via the USB port.
Your best chance for your 5TB drive working would be with a Android TV box that has USB 3.0 support, but even so, supporting USB 3.0 doesn't mean that your 5TB drive will work.
The best way to make sure that your drive will work is to use a powered USB hub that states that it has the power needed for your 5TB drive, but that is something you don't want to do.
If I had to take a guess your drive is probably going to want/ask for 5 volts at 900ma and when you compare that to "regular" USB 2.0 "rated" for 500ma, or half an amp, means that a USB 2.x port won't be able to support your drive, unless it's able to provide more power than what the USB spec calls for.
USB 3.0 is able to provide that 900ma, and this is why I mentioned looking for a Android TV box that has support for USB 3.0, for the best chance of the box being able to power your 5TB HDD.
You might try Googling "Android TV box with USB 3" do make sure that any box you find, says that it supports any "services" you want to use, like Hulu, Netflix and the like, a "Google certified" Android TV device should support "everything", be careful, because some of the boxes that come from China that have really great prices, might be running regular Android, and not Android TV, which will leave you with a STB that isn't what you expected.
I hope this made sense and was helpful.
Best wishes and good luck!