Wilson's New Reel for Five may be found in the first (1808), third (1811), and fourth (1822) editions of An Analysis of Country Dancing. Presumably it was included in the second edition as well, but I don't have a copy of that one to check. It also appeared in Wilson's The Complete System of English Country Dancing (London, c1815), from which the diagram above is taken. In its presumed first appearance, in the 1808 edition of Analysis, it is non-progressive, once through and done. I don't consider that to be very interesting. But in the other three manuals I've listed, Wilson suggested a progression that allows each dancer in turn to take the center position, making for a dance that is longer and more entertaining to dance but considerably more confusing to track.
And now comes the fun part: the other nineteen repeats!
Wilson does not discuss steps for Scotch reels, so I use my best available option, the steps given by Scottish dancing master Francis Peacock in his Sketches relative to the history and theory, but more especially to the practice of dancing (Aberdeen, 1805) and the common workhorse setting step, the pas de basque. I've described them before, so I'll just link to my previous posts. The starting foot is always the right foot for everyone.
For heying, crossing, circling, and leading under and around (first, third, and last eight-bar figures): Kemshóole steps, one per measure.
The dancers holding up their hands (First Partner and their neighbor to the right) should use twelve Minor Kemkóssy steps to dance in place as the other dancers lead under, switching to two Kemshóole steps on the last two measures when the neighbor is basically turned in place and the First Partner moves forward into the circle. This is similar to the way the lead-under figure works for the center and anchor dancers in my reconstruction of Wilson's New Reel of Three.
For the setting (second eight bars): any of Peacock's setting steps or a simple pas de basque are suitable, but my preference is for the Minor Kemkóssy. It is particularly suitable for the center dancer, who on the last two bars of setting must back up into the circle. This is exceptionally easy to do with four Minor Kemkóssy steps, though it also can be done fairly easily with two Single Kemkóssy or, a bit less easily, with two pas de basque. Other options for the edge dancers would include four pairs of Seby-trast or Lematrást steps (each takes one bar) or some combination thereof. I recommend that the edge dancers avoid using the Single Kemkóssy, since the poor center dancer will find it easier to orient their setting if the edge dancers are not adding a lot of sideways back-and-forth motion. Backing up into their place in the circle is also considerably easier if the two dancers they are moving between are dancing in place!
If doing this reel as a performance piece, it is more aesthetically pleasing to have all the dancers around the edge, at least, matching their setting steps. But a Scotch reel is also an opportunity for individual improvisation, so once the reel is mastered, then if dancing it socially, as long as the center dancer is able to get to their place in the circle (Single Kemkóssy, still a bad idea for the edge dancers...) and everyone ends up on the correct foot, have fun!
There is no specific music for the New Reel of Five; any period reel will do.
If it is danced 1808 style, once through with no progression, it requires thirty-two bars played once through. If it is danced progressively to the point where the original center dancer is back in place but the edge dancers have moved one spot around, it requires five times through. Halfway around, ten times through. And if it is danced progressively to the point where every dancer has returned to his or her original place, the sequence requires thirty-two bars of music played twenty times through, giving everyone a healthy ten-minute cardio workout for the day.
I don't have, or know of, any recording of a thirty-two bar reel with twenty repeats, so for the fullest version of the dance, one would need to either use live musicians or loop a recording to have enough repeats. One could, of course, also just stop at any intervening point (ten repeats, edge dancers halfway round, is nice), if one doesn't mind not getting everyone back to places.
Special thanks to my long-ago test dancers: Nora, Irene, Juliette, Kat, BDan, Alexia, Shelby, Lauren, and Marci!