To paraphrase several readers of Jaime Emerson's excellent site, B3 Bouldering, "Why 5? Why not 10? Why not 20?" And to paraphrase Jaime's answer, "Because it's my site and my list."
Any more questions? Ok then, on with the show.
Let me start by saying this... if you go to the gym just to have fun, with no desire to improve, then you should go and do exactly that. You should climb. Do whatever you want. Treat it the same way you do when you go outside. Just climb.
If you want to improve, you should definitely not go to the gym to just go climbing. If your goal is to treat the gym as "training" for climbing, then you'll have to structure it differently than you do your outdoor sessions. If your normal routine is to warm up, sample a few climbs, see how the project "feels" today, and then do 3 laps on the same 5.10... STOP. Do something different. Anything. Spend the night working on a project. Spend it on vertical topropes instead of leading the roof again. Go bouldering. And whatever you're doing, try hard. Learn something and take note of what you learned. This doesn't have to be an endless treadmill. If you do it right, it could get you somewhere.
Staying In Their Strengths.
When I look around the climbing gym, it's always the same people on the same angles. The crimp masters post up at the near vert walls. The compression junkies find all the biggest slopers and stake out the aretes. Those opposed to footwork are campusing up the steeps. It never fails. Hooray, you did another 45 degree V9 sloper rig. Good job. But why do you keep telling people that the 15 degree techy balance problem is awkward and stupid? Because you suck at it, that's why. Which is precisely why you should be doing it.
It's true, your hardest outdoor sends will likely be the ones that suit your strengths. However, the level of return you'll get on climbing solely at a particular angle or always on a particular grip will diminish rapidly. Paying closer attention to your weaknesses will make you a better climber. No question. And what happens when your ultimate compression project ends with a runout, techy headwall?
You'll wish you had spent more time on those awkward, stupid problems.
Counting Pitches, Discounting Quality.
Often when I ask people how their session went, I get an answer that details the number of pitches they climbed, as if they're in direct competition with Alex Honnold or they're training for the 24HHH. There's no mention of how hard they were trying, whether or not they learned anything new, or if they made progress on something. Only a confirmation that they reached their arbitrary number of scheduled pitches for the session.
Again, let me say this: If your goal in climbing is to get in a predetermined number of pitches each time you climb, and that is enough to make you happy, then by all means, keep doing it. I wish my goals were as simple to achieve. I envy you. However, if you want to improve at rock climbing, then somewhere along the line you got bamboozled into believing that a certain number of pitches is directly related to getting better. It isn't.
Well, that isn't entirely true. Sometimes it is directly related. When you are a beginner, or new to route climbing, then it may very well be to your benefit to get in lots of pitches. If it's early in the season and you're getting your route legs back under you, I'll give you a pass. But if it happens every week, your pass is revoked.
Instead of concerning yourself with number of pitches, try paying attention to the quality of the pitch, and the quality of the rest between pitches. If you're cramming 24 pitches into a 3 hour session, it's likely that you aren't rested well enough to give 100% to either your physical, mental, or emotional performance on 23 of those pitches. If the desire is to improve, I would rather see someone give 3 high quality attempts at a hard project or a climb that exploits their weaknesses than send 15 pitches at the same grade they've been climbing at for the past 5 years.
Quality, not quantity.
While I used to be a staunch traditionalist (ethical midget), I now see the truth. There is a time and a place for saying "Take" and sitting on the rope. While working out moves. While warming up. For (actual) safety reasons.
There is also a time and place when "Take" should be completely removed from your vocabulary. While in redpoint mode. While onsighting or flashing. While training.
If you're on a rope for training, it's likely that you're doing one of two things... an "ARC" type workout in which you should never get near the point of failure, or a workout that requires reaching failure to affect adaptation. In either case, unless for safety reasons, the word "Take" has little place.
The gym isn't only a training ground for the physical aspects of climbing. Perhaps more important for many of us, the gym can be where you get to hone your mental and emotional skills. Learning to go for it in the gym can make for much more productive days outside. For the many of you who find that several days are spent on your project just convincing yourself to make the next move or clip, it can be a major shortcut to sending.
Use it when appropriate, but when you're ready to go hard, forget the word entirely.
I used to be you. I "trained" solely on routes. I mean, I wasn't a boulderer, so why waste my time on bouldering? Essentially, routes are a bunch of boulders all stacked on top of each other. Sometimes those boulders are stacked in your favor, sometimes they aren't. In every case, sending depends on how efficiently, if at all, you can do the moves. It all comes down to strength and power. If the hardest moves on a route are at your utmost limit, it's unlikely that you'll send, and the best way to get better at harder moves is to try them bouldering.
You can absolutely work on difficult moves on a rope. However, even if you've mastered the art of trying 100% despite the fall potential, you've climbed a number of moves just to get there. You'll use energy to pull back up the rope. It takes more effort. It takes an excessive amount of time. Stop wasting time and energy, and work on hard moves right on the ground. There is no better way to get stronger.
I've heard many route climbers claim that they've never been shut down by a move, so there's no reason to train bouldering. Either you're abnormally strong, or you aren't trying routes that are difficult enough. I'd guess the latter. Even if you've never encountered a move that you can't do, gaining more power will make all those moves seem easier. You'll be less depleted for that last move showdown, or you'll have more left for the pump fest following that first bolt nerd gate.
More power can't hurt, but less power certainly can.