15, 10 and 5 RM refer to the rep maxes for each particular exercise:
15RM = 15 rep max, the weight in a specific exercise which is heavy enough so that you can do only 15 reps before failure.
10RM = 10 rep max, the weight in a specific exercise which is heavy enough so that you can do only 10 reps before failure.
5RM = 5 rep max, the weight in a specific exercise which is heavy enough so that you can do only 5 reps before failure.
For example, given an exercise such as Bench Press, you may have the following 15, 10, and 5 rep maxes:
15RM = 115 lbs.
10RM = 135 lbs.
5RM = 160 lbs.
Each exercise will naturally have different RMs, so you have to find out what your RMs are by trying them out.
15's, 10's, and 5's refer to the two-week blocks of training:.
15's = the two weeks where you lift your 15RM weight
10's = thw two weeks where you lift your 10RM weight
5's = the two weeks where you lift your 5RM weight
But you don't actually lift your real 15RM during all of the 15's. Instead, you start lower than it, then you progressively add load. For example, we made 115lbs our 15RM for bench, so during the 15's, we would be lifting (as an example only):
Week1 Mon = Bench 90 lbs for 15 reps, 2sets
Week1 Wed = Bench 95 lbs for 15 reps, 2sets
Week1 Fri = Bench 100 lbs for 15 reps, 2sets
Week2 Mon = Bench 105 lbs for 15 reps, 2sets
Week2 Wed = Bench 110 lbs for 15 reps, 2sets
Week2 Fri = Bench 115 lbs for 15 reps, 2sets
After Week2 Friday, Week3 and Week 4 is for your 10RM. You do the same. The 6th session is for your real 10RM (135lbs in our example), 5th session is 130, 4th session is 125, 3rd session is 120, 2nd session is 115, and the first session is 110 pounds for 10 reps, 2 sets.
After that comes the 5's, and you do the same thing.
When you reach your real 5 rep max, you continue it for another 2 weeks, and here you can add negs or drop sets.
After 8 weeks of training, you stop for 2 weeks (a mini vacation called strategic deconditioning) so that your muscles will be responsive again to lighter loads, and then you start the cycle all over again.