whether you are doing one of the many specific "5 by 5" programs that are around now or not, the same basic principles of progression apply.
when you start anything new, be it a new workout, new exercise, or new rep range in your training, start conservatively. for instance, if you were to begin to military press, and you were doing 3 work sets (not including warmup) of 5 reps each, and felt you could probably succeed with 150lbs, you should probably start with something more like 135lbs, and go up a steady 5lbs a week for the first 3 weeks... youll not fail, the workouts will be fairly comfortable, but will get progressively harder. after the third week when you do 150lbs for 3 sets of 5, decide if you think you have 155lbs in you the next week. if your sets were relatively easy, go ahead and try for 155 the next week, if they were hard, just go to 152 or 153lbs... judge how much you increase each week by what you feel you are capable of. at some point you wont get all the reps. say you get 5 on the first set, 4 on the second, and 3 on the third when the weight has gotten to 160lbs. then you would stick to the same weight the next week, and hopefully get all the reps or at least get closer. maybe youll get 5, 5, and 4. if so, keep the weight the same the next week, and again try to get all 3 sets. if you get them all, add a couple of pounds for the next time,
If you go a couple of weeks without getting closer to succeeding with all your reps, say for 2 weeks or 3 weeks you do 5, 4, and 3... then make a change. change to 1 work set, change to 5 work sets, change the reps, just make some change. and, start over with that new rep range, or new number of work sets, again with a weight that is comfortable, and again make steady increases, follow the same progression you did the first time.
if you have one week where you actually do LESS than the week before, say you did 5,5, and 4 one week, and the next you do 5,4, and 2... then immedietly change something and start over.
there should be NO subjectivity when selecting weights or deciding when to move up, NO going by how you "feel". if you get all the reps the week before, you move up, simple as that. if you dont get them, you try again with the same weight. if you go nowhere for a couple of weeks or decrease, you change the nature of the workout.