I don't buy sets I buy individual taps and matching dies starting at 1inch and working my way down as I can find them.
Not saying they don't exist because about half of the most recent taps and dies I've bought a thread dimensional chart for them can not be found in any of my several additions of the Machinery's handbook. A 3/16-20 would be a very coarse thread 24TPI is the standard coarse for 3/16", However I have found a 3/16-20 TPI acme threaded rod.
Having personally made many thread measurement mistakes in the past are you absolutely certain about the M5-.125. Thats sounds like the 5/8-12 I ran onto a while back that I thought didn't exist until I found the tap and die on ebay Like the stupid thread on the quill of my Mill there just isn't any quill nuts or bearing shaft nuts that match it in anybody's system. I wound up single pointing a pair of nuts to match the quill shaft and they worked perfectly.
If yoiu are absolutly positive of the size I'll keep researching, and hopefully come up with something

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