I train to failure every workout.
I do not associate failure with not being able to get another rep. If you look at how a muscle contracts, it is on the All Or None principle. Meaning all fibers contract or none. You don't contract half the muscle. You contract what you need (all) in order to lift the weight. Or you contract none and don't lift it.
If you are doing presses with 100's dumbells and you reach rep #7 and can not get another one (#8), that does not necessarily mean that you have reach muscle failure. You have reached rep failure, meaning you can't get another rep with that weight because you do not have enough (refreshed) muscle fibers to contract hard enough to raise the weight. But immediately go down to the 90's dumbells and you can get more reps because the 90's will be light enough that the remaining muscle fibers that didn't fire on the 100's (remember the All Or None principle) will be able to squeeze out 2 more reps. then no more.... if you go lower in weight, you reach the remaining few muscle fibers... and etc... and so forth.
Not being able to get another rep doesn't mean you have reached failure, it just simply means the weight is too damn heavy at that point.
With this in mind, before you go into the gym, do you poke your muscles and say "hey guys, listen up. We only gonna do 5 sets today, so I need you all to get with it. I ain't got time for 6, 7 or 10 sets, so lets keep it down to 5". This is where the pitfall lies when people post a thread asking "is XXXX number of exercises and XXXX number of sets enough?" Who knows?
Muscle failure, not rep failure, not cardiovascular failure, etc.. is the name of the game here. For some of us (like myself) who have - nor want - a training partner, we are unable to incorporate the high intensity techniques like forced reps, negatives, etc... that can allow us to reach muscle failure with a lower number of sets. Not only that, but as I stated before, for me - negative and forced reps are nothing but wear and tear on my joints and stabilizers, especially at my low bodyfat condition. I would rather do more sets than wake up the next morning with tender and aching joints.