I am pretty certain there is nothing special about these five movements, even though they provide a gentle workout. They resemble, but are not directly connected with the यन्त्र(Yantra) type of Yoga. In Sanskrit, Yantra means something akin to motor or machine. In practical terms, it has flowing movements training the motor functions of the body. Contrast this with the more static Hatha Yoga type of Yoga that appeared some centuries later. As Yantra Yoga appeared in Northern India around 7-9th Century CE, it also made its way into Tibet when Buddhism spread into those regions.
There are some manuals on Yantra Yoga written in Classical Tibetan. That's how I know that they somewhat resemble these five movements that Peter Kelder popularised decades ago. For reference, the only English Translation of a Cycle of Yantra Yoga was published by Namkhai Norbu("Yantra Yoga")
That manual also gives some indication as to what that mysterious 6th rite is supposed to be.
Basically, Peter Kelder really put me off when I first read his book about the Five Tibetans. Typical myth-making story, harkening back to the days of Blavatsky and also to a certain extent, Gurdjieff(the "met a high-level esoteric teacher but won't name him nor what tradition he is from" pattern; makes for great stories but isn't exactly helpful in determining what is credible and what is not)
To clarify what has been written in the OP, Peter Kelder makes the claim that the guy who introduced him to the five movements was a retired army type who just happened to learn these practices in a Tibetan Monastery, where residents apparently slowed down their aging process. Kelder meets the army guy several times and is shocked at how young he appeared to be in the second encounter, despite his stated age.
Of course, he links the rejuvenation effect to the exercises. No in-depth details are given about the 6th movement, which is named as critical to the rejuvenation process. At least he gives the hint that celibacy is a necessity for the 6th movement.
That's basically the story.
Now, for the clarification of the 6th Movement and the ideas behind it.
It's about "sexual energy redirection". Tibetan Buddhists, like their Indian ancestors in terms of teachings, think in terms of energy. You need to keep this in mind if you want to understand this. The basic motivation was that celibate monks became frustrated with sexual restraint and sought a way to make use of this energy that just kept building up as more food was digested. Those who didn't want to use sheer willpower in defeating sexual cravings made use of bandhas(Sanskrit for muscle locks) and breath retention exercises which they noticed to somehow redirect the problem in an upwards direction.
A side effect was also a clearer mind and lots of heat. This gave rise to the gTummo type of exercise that appeared in the Six Yogas of Naropa. This is how practitioners can melt snow or dry wet clothes on their backs.
The heat was a useful side-effect for the cold climate of Tibet, but the actual exercise was for inducing altered states of consciousness and forcing this energy into the "main channel"(sushumna in Sanskrit) which produces all sorts of effects useful for the mind bent on seeking knowledge.
Since I practice this myself and have received this teaching for other practitioners, I can state that it has a rejuvenating effect, most likely due to the better distribution of oxygen as a result of the breath retention and stimulation of the nerve plexuses if you want to dismiss the energy dynamics of traditional Indian/Tibetan/Chinese metaphysics. From what I've gathered from others and experienced myself, it gives rise to these effects: Clear, cool mind, deeper abdominal breathing, shiny face, resistance to cold. If it truly slows down aging itself, I cannot say because I would have to see large groups of practitioners over several decades and compare them to non-practitioners to gather any useful data. And Kelder is right, you have to be celibate for it to be effective, because in these traditional schools, the sexual energy is the fuel which you use to improve your well-being. That's also why practitioners will consume lots of fatty meat if they have access to such things.
The actual exercise is divided into two parts. The first part is about contracting the perineum area(seat of sexual energy according to traditional view), the abdominal area(lifting it up) and the throat region(lowering the head so that the chin touches the base of the throat) and performing a slow, long inhaltion similar to pipe breathing, holding the breath for at least 120 seconds and then violently shooting out the breath through the nose. Gradually extending this to up to several minutes, even though we now know that beyond the 2 minute mark, brain cells may die. This will trigger shaking in the body, strong perspiration, heat and interesting states of mind induced through O2/CO2 imbalance in the brain. So the initial flush of heat is most likely due to a panic reaction of the brain that attempts to increase bloodflow to provide better oxygenation to the body.
This triple muscle lock(basically Maha Bandha of Hatha Yoga) combined with long breath retentions can rejuvenate your mind and body for quite logical reasons, even without going to Stage 2 of this exercise which involves elaborate visualisations that aid this process.
This most immediate effect is a suspension of mental chatter since breath is said to be directly linked with consciousness which is also linked to the body's internal energies(traditional terminology). So if you suspend the breath, the mind will come to a halt, which will likely induce the internal energies, which will improve your health.
That's the basic outline. Of course, this is far more complex than Kelder made it look like and it certainly isn't an easy morning routine so I wouldn't recommend practicing following my short description alone.
But I think it should be obvious that the effects Kelder talks about are likely derived from this 6th exercise and not from the 5 movements, which are an exercise of the motor functions of the body, which, in themselves, may not produce the effects of Kelder's hype, but carry all the benefits of normal physical exercise nonetheless.
