2: Great weapon mastery does *not* give you a flat out +10 damage. It reduces your chances of hitting, so your effective damage bonus is far less than 10. Furthermore there is the opportunity cost of taking a feat instead of an ASI. Lastly feats are optional - this will not be possible in every game.
But will be possible in many games. Let's face it - what player interested in DPS and optimization plays without feats, eh?
Anyway. What GWM does is give you a flat bonus of +10 to your base damage. To all your attacks. Which means that the character best suited to benefiting from this is the character with:
* many attacks
* that each deal comparatively little damage
The paladin is not that character, nor is the rogue. They make too few attacks, and they are able to deliver great base damage on their own (which makes the -5 not worth it).
The character you should play when you pick GWM is the
fighter. Preferably a fighter that you can count on making four attacks each round at around 10th level, increasing from there.
Then, back to the +10 part. That it increases your base damage is fact. No miss chance in the world can change this.
So all you need to do to break this feat is... to not miss. This is actually easier to accomplish than you might think, and certainly easier in practical play than all those whiteroom DPR calculations would suggest.
First off, you absolutely need Advantage. I don't care from where. You don't use the -5/+10 part without it. Monk Stun? Faerie Fire? Monster shoved prone? Don't care how. It's the first and most basic party strategy, to consistently be able to produce advantage against the foes you attack. A party focussing its attacks on the foes that give them advantage, and
only that, is already playing at another level than the naive party where each member fights his own personal battle.
Put bluntly, if it becomes your turn, and there is no foe which grants you advantage, it is your job to create one for your friends. Otherwise you're doing it wrong.
Then you need a way to turn near-misses into hits. One simple suggestion is to play a Battlemaster and use Precision maneuvers. Remember, you only need to spend one of these when you experience a near-miss. (Then feel free to enter things like Bless or Bardic Inspiration into the scenario if you like).
If you roll a "2", chances are adding something like a d8 will still miss, so write that off as a true miss.
If you roll a "1", well, you took the Lucky feat (or played a Halfling), right?
All in all, you should find that the -5 part that whiteroomers calculate as, what, a 40% drop in actual damage is hilariously inaccurate, and severely underestimates the power of the feat.
More likely is that half your rounds against AC 18 or lower you will hit will all your attacks, and you will enjoy the full +40 damage boost. (And note the aggressive AC value cited. I bet you the WotC designers thought the feat only useful against really low values of AC even at high levels...)
Since there is nothing else in the game that comes even close to that number, GWM is patently broken. At least in the hands of a competent minmaxer.
Then there's the SS/CE combo, which is even more broken, but that's another story.
Point is: don't waste GWM on characters with few high-damage attacks. Of course you will feel like the feat isn't all that good. Just a tip.