This sounds a lot like Body by Science. Instead of 5 exercises done every 7-10 days, it’s 12 exercises done three times a week. It’s roughly the same time per week. My understand of the aforementioned book, though, is that exercising more often will slow strength gains. The 7-minute workout might be optimizing for something other than strength, of course. Of course, how it works for you matters more than any results from a study.
The Scientific 7-Minute Workout – NYTimes.com
In 12 exercises deploying only body weight, a chair and a wall, it fulfills the latest mandates for high-intensity effort, which essentially combines a long run and a visit to the weight room into about seven minutes of steady discomfort — all of it based on science.