The WALTZE À CINQUE TEMPS --- This Waltz was done around 1845 by Jules Perrot. The only information I can really find on this dance is copied below from La danse des Salons by Celarius. I have copied the whole page here for you, exactly how it was written in 1847.
Danse des Salons page on "WALTZE À CINQUE TEMPS " by Henri Cellarius (1847)
Le Maelzel's Metronome, 152 (note: probably 152 bpm's)
I will finish what I have to say upon the different kinds of waltze, by giving some account of a new waltze composed, during my residence in London, by my friend, Perrot, and which he has had the kindness to dedicate to me, I may therefore say I have been at the fountain-head to acquire its execution and principles. This, which is called the waltze à cinque temps, is as yet known in Paris only by hearsay. I must therefore confine myself to a mere technical notice, and wait till it has received the approbation of the French public
before making any peculiar observations.
The step of this waltze in itself has nothing very complicated; the principal difficulty consists in the time, which is little used, but of which nevertheless we find an example in Boieldien's celebrated air, "Viens, gentille dam e." The pupil should in the first place familiarize his air with this time, and after attending to it for a little while he will be able to keep it as easily as that of the other waltzes. The waltze à cinque temps, destined originally for the theatre, was executed by springs, and was composed of many figures and running steps, which have been suppressed to make it suited to the public. The position is the same as for the waltze à deux temps; the gentleman begins with the left foot and the lady with the right.
This is the detail of the five beats, of which the entire waltze is composed;
First beat: the waltzer should have his right foot in advance, make a jetè with the left, passing before the lady as in the waltz à trois temps.
Second beat: place the right foot in the third position behind.
Third beat: join the left foot behind the right.
Fourth beat: place the right foot in the fourth position in front.
Fifth beat: A little glissade behind and on the side. It is necessary always to recommence with the left foot.
A demi-round must be made to the three first beats as in the waltz à trois temps; you then make a slight turn to the fourth, and make the second demi-round upon the little glissade. I shall now point out the lady's step, decomposing the five times as for the gentleman.
First step: The lady should have the left foot in advance, and make a jetè upon the right foot, raising the left foot behind.
Second step: Coupé upon the left foot, raising the right foot before to the fourth position.
Third step: Jetè upon the right foot, raising the left behind.
Fourth step: Jetè of the left foot, raising the right behind.
Fifth step: Little glissade behind the right foot.
The lady should not forget that she must always commence with the right foot. This waltze is capable of as many variations as the others, and admits equally of l'envers and l'endroit. To accustom the pupil's ear to this time, the composer has suggested a bell to be struck with a little hammer at the fifth beat. For the greater facility this measure may be divided into two: -- a measure of three beats, and a measure of two.
After this simple detail, made rather by way of precept than for the world, I do not pretend to give any farther idea of the waltze à cinque temps , nor to presage the less or greater success, that it is destined to meet with. If, however, I may be allowed to speak of my personal impressions, independent of the fascination it derived from the wonderful execution of its inventor--it seems to me to combine all the conditions of allurement and grace, which are needful to put it on a par with other dances and new waltzes. I think too that there will be found in its execution a peculiar originality, which it owes to the piquant clashing character of the rhythm, which may perhaps above all contribute to its becoming fashionable.
But I must not forget that I am talking of a waltze which so to speak, is unpublished, and which, at the moment of my writing, has not yet appeared in any French ball-room. I have always held the maxim that a professor of dancing should never take the initiative in the matter of a new dance or waltze; he ought to wait for the public impulse without ever attempting to give it himself. A master's pretending to impose a novelty on the ball-room might perhaps be enough to drive it from them for ever, whatever else might be its merit and attractions. It is, therefore, under the form of a mere suggestion that I have ventured to speak of the waltze è cinque temps, I have therefore endeavoured to describe its fundamentals, and to explain the step for those who may wish to try it. My duty now is to watch for the first indications, and to see what may be its fate in the balls of the ensuing winter ."