The rep rate of 5 with increasing weights is usually described as a rep range for muscle hypertrophy.
Hypertrophy is difficult to come by, with five pounds of added body muscle per year being a much above average gain. Easy to back off if you should see too much hypertrophy in any muscle.
When you begin exercising the first
considerable strength increase, maybe over several weeks or a few months, is said to be mostly due to your nerves and muscles adapting to work together to produce more strength, not much real hypertrophy. After the nerve adaptation phase if you increase weights farther the next adaptation is hypertrophy.
There may be an increase in the size of blood vessels for some rep ranges, again not exactly muscle hypertrophy. For that rep range I believe that the 'pump' will swell your muscles during and for maybe a few hours after you exercise. Maybe more the 12-20 rep range. ?
Speculating - I have suspected that if you exercise using very heavy weights, for some days there may be damage and swelling in the muscle, a little size increase. That temporary size increase, if it really occurs, would not be true muscle hypertrophy.
For hypertrophy an approach for reps is to do 8 reps with a weight that is very difficult to do on the last rep (or to failure??). Gradually increase to 12 reps always with the last rep being very difficult or failure. Then increase weight, drop back to 8 reps and repeat.........
There is a very well know relationship between the most weight that you can lift one time, 1rep max (1RM), and how many repetitions you can do with a weight that is a percent (0-100%) of 1RM. There are many calculators on the internet.
http://www.exrx.net/Calculators/OneRepMax.html
Rules of thumb for reps related to 1 rep max.
You can lift 80% of 1RM 8 reps.
You can lift 75% 1RM 10 reps.
The simple relationship starts to become less accurate at reps above 12 or 15. Not applicable above 20 reps I believe.
Rep range information
http://weighttrainingexercises4you.com/rep-ranges-to-develop-muscle.html