I was buying new paintbrushes, and saw some labeled 10/0 and 5/0. They didn't really look any different than a 000 brush. Are they just a different ways of measuring the same length, like the metric/imperial measurements? Is a 10/0 the same thing as a 000?

I did some looking last night and I couldn't find a definative response.
I know the more 0's the smaller the brush in theory. Outside of that I'm not sure.

To my knowledge, brush size numbers aren't tied to any measurement systems and they aren't standardized, meaning that for example 000 sizes from several manufacturers can (and most probably will) vary.
The basic rule is 'more zeroes-->smaller brush'.
Those 5/10 and 10/0 seem to mark the number of zeroes, as it wouldn't be practical to mark brushes with 0000000000.

The smallest brushes I usually purchase are either 000 or 5/0, depending on the brand. When going smaller than that, the tip of the brush isn't any smaller, just the whole brush, making them harder to work with (they hold less paint, and especially acrylics dry up quickly on them). For some super-tiny details, I do have a couple of 10/0 brushes, but I rarely use them.