The 5 Couple repeat in 5 couple set is simply called a 5 Couple set since there is, as yet, no risk of ambiguity with any other Longwise set format.
The Full set requires five Couples and the dance usually consists of five Repeats, each involving all five Couples, with each Couple dancing once through in each Place. Although all are involved, usually two Couples are the Dancing couples. Most commonly, these are the 1st and 3rd couples; at the end of the first Repeat, the Progression usually leaves the Couples in the order 2 4 1 5 3.
In an alternative Progression, where the 2nd and 4th couples are the Dancing couples, as in St Columba's Strathspey, the Finishing order is
3 1 5 2 4.
In at least one dance, Miss Johnstone of Ardrossan, the 1st couple is the only Dancing couple of the Active set and the Finishing order is 2 3 4 5 1. In another, Caddam Wood, the Progression for the Men leads to 2 3 4 5 1 while that for the Ladies is in the opposite direction, Finishing 5 1 2 3 4; at the end of each Repeat, the dancers have new Partners, only meeting their Original Partners on the final bar.
For example, here are some Scottish Country Dances in which the term, 5 Couple set, is used in either the Minicrib or the Maxicrib Dance instructions or both -
A Flock Of Geese