I've searched high and low for this, but all I could find was articles on the best number of reps and sets (rep and set range etc.)
But how long should one rep be for maximum hypertrophy, given, say, a 5x5 routine (does that change for more reps/sets?)?
Additionally, what is the most effective rest period between reps within a set?
Of course this depends on the individual, as does everything else, but are there any studies or recommended values?
Lifting fast will make you stronger, but strength is not hypertrophy. However, strength will help you increase volume, and volume is one of the primary causes of muscle growth. For more on volume's relation to hypertrophy I recommend Strengtheory's article on volume, which has plenty of references. The bottom line there is that hypertrophy is largely determined by the number of challenging (read: to failure or near-failure) sets.
My recommendation for someone doing a 5x5 with the goal of hypertrophy is to do the reps relatively fast. It's even recommended for strength gains to be explosive, even on "slow" lifts like the squat. This helps with recruiting fast-twitch muscle fibers.
As to the time between reps within a set, I'd recommend not referring to this as "rest", since that confuses the issue with actual rest periods between sets. It also doesn't reflect how that time should feel: if standing with the bar on your shoulders during a squat set is easy, you're not squatting enough. It should be slightly taxing. But time-between-reps-within-a-set should be between half a breath and a few breaths. For something like squats or presses, where you're bearing the weight between reps, it's really up to you regardless: if you're doing a 20-rep squat set and want to take ten breaths between rep 18 and 19 (and you should!), then go ahead. It doesn't make rep 19 any easier or less effective. For exercises where you're not bearing the weight, try to keep that time minimal, within the context of "a few breaths". For example, if between deadlift reps you take five breaths at the bottom, then it's not really a single set anymore because you're taking true rest.
My philosophy has recently changed on this in as far as I was thinking in the terms you are thinking of - what is the magical combination of reps/sets and rest. This doesn't matter so much. A person who is cardiovascularly more fit than you (I.e they have more stamina and endurance) will be able to do higher reps and sets than you, but really they are both means to achieving the same goal -- complete teardown of the muscle fibers.
That is basically the only thing that matters. Are your workouts completely tearing down those muscles and working them to failure so that you force your body to adapt and rebuild them larger for next time? (And as a given, do you have the proper nutrients in your system for this process both pre -during and post workout? protein, carbohydrates, glycogen, vitamins, micronutrients)
It doesn't really matter how one gets there, just tear those suckers down each time and they will come back stronger. Just remember you can't do the same thing over and over and expect the same gains, so you will need to add variation to your workouts to cause the muscles to adapt and change again.
What I suggested on most of my posts, is to figure out what works the best for a person. What works for me, may not work for you, as we are all different. Some studies say something, while others say other things, because they are performed on different people, and as everyone differs, so do the studies, unless they are based on some basic rules.
Regarding the length of the rep, there is no basic rule, as it depends on what you are doing. Some people do explosive workout(for example the cross-fit). There every rep is quick and explosive, but that can't be done with super heavy lifting, which requires proper form and balance. Whatever is the case, you need to find out what feels the best for you, and also, what your body can handle. So, trying out different things is the only way to figure it out.
