These feats are not meant to be a simple DPR increase
(In many cases they are actually decreasing DPR)
If you want that, just take the Ability Score Increase. Great Weapon Master and Sharpshooter are not meant for every situation, as proven by the calculations below. It is more of a way to convert excess hit chance to damage.
Even if your calculations show that GWM is beneficial, because you are fighting a prone, naked elf, you should consider that it wont be any more dead from 20 damage than from 10, when it has only 1 HP.
If you impose any conditions on a hit (prone, poisoned, frightened, etc), it might be more benefitial to attack without the -5.
When should you take the feat?
If your allies have a way to reliably provide Advantage for attacks, you just take the feat.
1st level: Human Variants could take it, but unless you are playing the Zombie Apocalypse, don't. With your low hit chance against the usual opponents, you will not have the opportunity to use it very often. Polearm Master / Crossbow Expert increases your DPR much more often.
4th level: A Battlemaster Fighter can quite reliably prone with Trip Attack. From level 5 it is possible to attack normally and prone, and use the second attack with -5/+10. Otherwise an Ability Score Improvement provides better average DPR increase.
8th level: Same as level 4.
12th level: This is where you should take it, and only because you can not increase the ability above 20.
Efficient adventuring groups have ways to provide Advantage for heavy hitters, the above advice is only meant for the less fortunate.
Level 4, Greatsword, Great Weapon Fighting Style, Strength 16. Is GWM better than ASI?
Attack: +5 (Str 16, Proficiency +2)
Base damage: 11.33 (Great Weapon Style, Str 16)
DPR vs AC 12: 7.93 (0.70 x 11.33)
DPR vs AC 15: 6.23 (0.55 x 11.33)
DPR vs AC 18: 4.53 (0.40 x 11.33)
Attack: +6 (Str 18, Proficiency +2)
Base damage: 12.33 (Great Weapon Style, Str 18)
DPR vs AC 12: 9.25 (0.75 x 12.33)
DPR vs AC 15: 7.39 (0.60 x 12.33)
DPR vs AC 18: 5.55 (0.45 x 12.33)
Attack: +0 (Str 16, Proficiency +2, -5)
Base damage: 21.33 (Great Weapon Style, Str 16, +10)
DPR vs AC 12: 9.59 (0.45 x 21.33)
DPR vs AC 15: 6.40 (0.30 x 21.33)
DPR vs AC 18: 3.20 (0.15 x 21.33)
Crit: 0.42 (0.05 * 8.33)
In most cases ASI gives you a better DPR than GWM.