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The thread shouldn't be worn, given it's a brand new frame (which does beg the question why a frame builder would use a part containing obsolete threading).
Given that I can find no cable adjusters using imperial threading at all, it looks like my best option would be to tap the thread out to M6, which I would assume should be possible?
Jon.-
tap the thread out to M6, which I would assume should be possible?
If the major diameter of what's already there is well over 5mm, an M6 thread will be weak as the proper drill size is 5.0mm. I tap oversized holes out to M6 all the time for keeping my wheels in the frame, but they're not significantly loaded along the thread axis and the holes are only about 0.2mm oversize. You'll have to make your own judgement about how much oversize the hole is and how the load will interact with the ensuing reduced flank contact.
You could use a fluteless (thread forging) tap, but they are expensive to buy and hard to use. The correct pilot hole for a fluteless M6×1.0 tap is 5.5mm
gbj_tester
I can't tell you what to look for, but what you're probably looking at is a badly worn M5 thread. The best fit for something with a pitch close to 0.8mm and a diameter between 5 and 6 would be 7/32"×32TPI ME, and you could probably tap out an M5×0.8 female to that size quite successfully, as the flank angle is close enough and the pitch error is <1%