It actually promotes rather rapid strength gains, although you are right about the lack of hypertorphy.
Basically you do the program until you cannot complete the first set of 5. You never go to failure. So for example, to make things easy, let’s start with 100lbs. Say you can squat 100lbs for 10 reps. Your first workout would be
100 x 5, 5 min rest, 90 x 5
day 2: 105 x 5, 95 x 5
day 3: 110 x 5, 100 x 5
day 4: 115 x 5, 105 x 5
day 5: 120 x 5, 110 x 5
day 6: 125 x 5, 115 x 5
day 7: 130 x 5, 115 x 5 (note that the second set does not necessarily increase by 5lbs each workout, but instead is 90% of the first weight, rounded to the nearest 5lbs increment.
and so on, until say one day you were trying for this workout:
150 x 5, 135 x 5
But you only got 150 x 3 on your first set. You would then do 135 x 5 on your second set, but since you did not get 5 reps on the first set, this cycle would be over. Take a few days off, and then begin again a little higher than before:
105 x 5, 95 x 5
and so on.
This program is excellent for strength gains, but hypertrophy is minimal (unless you’re a total beginner).
It is more designed to increase the amount of tension generated by the muscles, as opposed to the size of the muscles. Hypertrophy does not result because the muscles are not being used until most of the fibers are worn out (as with bodybuilding training), instead, the load is increased.
If this method is used to reach failure, even though that is not advised, the failure is not due to intense “burning” as it is in a bodybuilding workout (like, “do this set to failure”), but instead the muscles just run out of energy. There is no lactic acid buildup.
I still disagree with you that heavy weights cause soreness. When I used to bodybuild, I would get MUCH more sore in the days following a workout because I used less weight and more reps (reps in the 8-10 range, i never got into the 12+ stuff cuz i didn’t like it). When on the above mentioned program, I never, ever got sore. Ever. Even on days when I maxed out and set new personal records, I felt like I could take on the world when I left the gym. When I was BB’ing, I would limp to my car after an intense workout of squats bodybuilding style.
But, use whatever works for you 
Good luck,
Iron