I own neither D5 or D500 so no horse to back if there is a race. Without comparing images of the same subject in the same lighting conditions comparisons are fraught with the potential for misinterpretation of resulting data. Not suggesting that this is the case here but just food for thought!
I do however find the notion of noise and comparison between the two cameras to be at odds with what I have seen (limited) and believe to be the case with these cameras. Bottom line is that there seems to be a very similar noise signature between the two cameras set apart by only one stop!
Example attached D5 @ ISO 12,800 compared to D500 @ ISO 12,800 and 6,400. The inset represents print size at 300 ppi. This appears to confirm the one stop difference with the D500 at ISO 6400 matching the characteristics of the D5 at 12800. Other ISO seem to be very similar. As already suggested it is possible that underexposure has affected noise and this coupled with the way that raw converters may apply base line offsets to exposure and screen presentation may go some way to explaining why some are seeing bothersome noise
Bear in mind the perception of noise will be changed by your monitor resolution intended output size and medium. Looking at a 100% view in PS or LR on the average resolution monitor will display an image 300% size of a print (most Canon/HP/Fuji printers ). As viewing distance seems to be irrelevant for photographers (get as close as your nose or belly allows - men only of course

) with the suggested 1.5 - 2.0x print diagonal always ignored you must make a print or section to judge the qualities of Noise reduction, Sharpening etc
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