I don't know squat about turtles, but think a 20 gallon long (30 inch by 12 inch footprint) would be the smallest tank I'd keep a 5 inch turtle in.
following my lack of knowledge of turtles and a bit of common sense, most of them are only semi aquatic, if aquatic at all, so for one, so that means they don't have the thing fish have where they can utilize the length, width, and full height of the tank.
For two, they're a tad bulky, length, width, and height wise, so of course they should have length and width at least to help them move around if they so please. Most fish only have length and height, and their width is less of a concern.
For 3, I wouldn't even keep a 5 inch fish in a 10 gallon tank anyway, so why would you keep a 5 inch turtle in one?
Unless told otherwise by a turtle expert, I think the 10 gallons per turtle rule is bull, like the 1 gallon per inch of fish rule. But that still doesn't mean you should keep one in a 10 gallon tank.