There are many variations.
For example,
5x5 across - do some warmup sets of lighter weights, then the same weight on all 5 sets. When you can do 5 reps on all 5 sets, increase the weight. And so on. This is the way Stronglifts.com does it.
But there's also
5x5 ascending, where the first sets are the warmup sets, and you make the top weight only on the last set, or last few sets. I believe Rippetoe's
Starting Strength uses something like this. I am doing a variation (see sig for journal) with 2x5 warmup sets, and 3x5 work sets on the same weight. For example, bench press 40kg x5, 60kg x5, then 80kg x3 x5.
There are also
different combinations of exercises possible. They all boil down to wanting to work chest/shoulders, back/arms and legs at least once in every workout: one
press motion for chest/shoulders, one
pull motion for back, and one
press or
pull for legs.
For example,
Bench press (press for chest/shoulders)
Power clean (pull for back)
Squat (press for legs)
or
Overhead press (press for shoulders/chest)
Squat (press for legs)
Deadlift (pull for back
and legs)
The reasoning behind
choosing 5x5 as the set/rep range is that there is some evidence that 4-6 sets of 4-6 reps per large muscle group is the best range for building strength. So to make it simple they make it 5x5, easy to remember.
It's also the case that when people become fatigued, their form on an exercise breaks down. Beginners have relatively poor form because they've not had the practice, so their form breakdown will be particularly bad. Thus, doing just 5 reps allows them to keep okay form for more of the 5-25 work reps they're doing. That's the theory, anyway.
Experienced coaches argue about whether something like 5x5 is best for beginners,
or something else - for example the
Beginner's programme Markos has posted up, something like that used from the 1930s or earlier. That's experience - they argue what's best, and each has a lot of strong lifters come out of their programmes.
That's experience, what about
lab science? Well, it seems that full-body or split, single or multiple set, 5 reps or 15 reps, it just doesn't make much difference if you take untrained people and have them do it for 6-12 weeks. So long as they stick to it, they'll get stronger. Some get stronger faster or slower, but remember that as well as the workout programmes they have diet and sleep and so on. A pair of identical twins on the same programme could get different results because of the other stuff.
From your post lordoftime, it seems you are effectively an
untrained beginner. So for you the exact programme you choose is not as important as that you stick to it! Consistent effort over time gets results.
After those first 6-12 weeks, then different set and rep ranges get different results, and which you go for depends on your goals. However, the differences are not as great as people sometimes make out. For example, "I want to train for size not strength," well have you ever seen the guys in strongman competitions? Not weedy