Since you said intermediate I'll assume you mean intermediate and will explain it to the best of my ability.
First of all, whether you can add to your maxes consistently after week 4 depends on how advanced you are in your training. But pretty much everyone, if they have never tried this type of training before, should have some success.
The main difference between an intermediate and an advanced 5x5 basically comes down to loading periods, or more accurately the period of time that is considered a training stress, after which recovery, in some fashion, is assumed to take place.
If you were a beginner you'd start with EACH workout being a "loading period" unto itself. You would train, recover in 24 to 72 hours (assuming proper programming) and be able to load the bar again right away. After a while, perhaps up to 9 months to a year, there would come a time when you were not able to progress this way anymore. Your strength would come to a point that the stress you were able to impose in one workout is greater than you can recover from before the next.
So at that point you are intermediate. Without getting into all the less efficient choices one could make to continue progress the next step is that a period of stress that encompassed one workout and recovery from that is now a longer period of time encompassing several workouts. For ease of scheduling (so you can have the weekends off
) that loading period becomes a week. It should be obvious now that the difference becomes the length of loading periods, or, the period of time you need to produce a significant training stress before full recovery takes place. So this is all simply a way of periodizing and obviously there are other ways to do that. This one just make a whole lot more sense than some.
I guess it would make sense to add the obvious and crappy choice, which would be pouding the hell out of it once a week and then waiting around for recovery to take place, hoping you did enough to produce an adaptive response and also hoping you time your next workout perfectly so that no fitness is lost. Basically guesswork.
For an intermediate 5x5, what I have described above is basically what defines it. Whatever way it is programmed within the week and however progression from week to week is designed to work, that is the basic crux.
Now on the intermediate 5x5 you are probably speaking of if you were to go into week one with loads close to maximal then it would be very difficult to add to your maxes for very long if at all, although it can be done. It would severely undermine length of time on the program and thus overall results and could also result in some overuse injuries at the end. Not a good idea.
The "theory" behind week 4 is called
intensity cycling. You are simply projecting you 5RM's and then cycling back the loads 4 weeks with the intention of arriving at those 5RM's on week 4. It's not a new concept. It's a pretty basic and primary means of progression. Working back up to the maxes in this fashion will pretty much ensure you can proceed past the original maxes and end up with a substantial gains in strength.
Along the way you are theoretically recovering from each week. Not just until week 4 but on beyond for no predetermined amount of time. The workouts within the week are designed to ensure both enough of a training stress to promote an adaptive response AND recovery within the week. You gain NEW fitness each week and DISPLAY that fitness the next week.
So in the light, medium, heavy or
Starr Model, the heavy workout is the significant stressor. The light is in there to allow recovery but to make sure there is not a loss of fitness. To paraphrase Rippletoe, it 'reminds the muscles there is still work to do'. And the medium workout is usually more intense but much lower in volume than the "heavy" workout. Therefore it allows progression to be spurred on, and you are displaying the gains made without significantly adding to the recovery debt of the week.
As you can see from 0311's description of the advanced programs, they are designed so that recovery does not necessarily take place within the week. So maybe on an intermediate format you would have one "volume" day and then perhaps a recovery and "intensity" day. But on the advanced (speaking of fullbody) you'd have two volume days and fatigue will not fully disipate but will be allowed to accumulate over a period of weeks.
Then you'd have a recovery and then an intensity or "peaking phase". Now that's all 0311's province. The only reason I'm speaking of it is if you look at my description of an intermediate week and an advanced loading period, you'll see that they are basically very similar. Only the time periods have drastically changed.
The "single factor 5x5" of Madcow's site is a perfect beginner/intermediate program. Perfect way to start. A beginner could also do it with good success although it would not be the best choice. The converse is not true, however, and a true intermediate would probably not do as well on a true beginners program.
As I said this 5x5 is great but it is simply an intermediate program. It's a good way to start but not the only way to do it. In fact the only rule is that it's periodized into WEEKLY PERIODS. If one can successfully add weight to the bar each and every week for a good period of time, that's all there really is to it. It's just that there are logical ways that that can be accomplished.
If you really know what you are doing you can react to what's happening and successfully manage fatigue and recovery for long periods of time resulting in tremedous strength gains. This program we are speaking of is designed as a cookie cutter and so is appropriate for a less experienced lifter. But because of that some fatigue will start to accumulate as workloads increase if no adjustment takes place.