As I understand the ATC standards are 1nm and 1000 feet. The tolerances are then added on depending what equipment is giving the info ie: RNAV, DME, radar, time etc. The radar 5nm is from what I remember from the tolerance of the normal ssr head at max distance (cant remember what that distance is) that being some 1.7(was a rating question i got from a certain overly officious check officer) degrees applied to both tracks which is 3.4 then rounded up to 4 then add the ATC 1nm standard and voilas 5nm. Here in AUS we have a 10 nm radar standard when the screen display is really big or the acft a long way from the head.
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