As Ray says, the TR5 was not legal in the US, for emissions reasons. The story I heard was that Triumph was originally assured that the Lucas fuel injection could meet US emissions standards, but when they built the car, it's tailpipe was too dirty. Lacking time and money for further development (which might never pan out); and knowing how to make the carbs pass emissions; they created the TR250 for the US market. The carb/PI dichotomy continued through the TR6, although they decided not to use a different model name after one year of the TR250.
In addition to the PI/carbs, the camshaft and compression were different. The TR250 also had a lot of extra trim and that strange stripe across the nose. But the TR250 is basically identical to the TR5.
There are a very few genuine TR5s in the US, though. I forget the name now, but there was an enterprising individual that was ordering them for delivery in another country, then disassembling them, shipping to the US as parts, and reassembling them here. As I recall, he went to prison for his efforts, but the authorities did not track down all the cars.
Charles Runyon, owner of TRF, has a genuine LHD TR5 (although I don't know how it came to the US).
Unfortunately, there are also numerous fakes; TR250s that have been converted to fuel injection (or in one case, just had the trim changed). Caveat Emptor.