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Great Weapon Master adds +10 damage on melee attacks that hit. Say I subtract my -5 and still hit. If I am a fighter and attacking 2 or 3 times in one action, do I add +20 or +30 damage, or stop at only +10 damage?

The +10 damage bonus does not cascade, but it does apply to each attack.

While there are often time/speed benefits to rolling attacks in groups¹ (some people like to use different colored dice), you still consider each attack separately. An 11th level fighter using Extra Attack will roll three separate D20s, evaluating hit or miss for each of them. After each hit, roll damage - any attack rolls you took the -5 penalty on get the +10 damage.

Compare the Great Weapon Master Feat's benefit...

Before you make a melee attack with a heavy weapon that you are proficient with, you can choose to take a -5 penalty to the attack roll. If the attack hits, you add +10 to the attack's damage.

...to a Barbarian's Reckless Attack feature:

When you make your first attack on your turn, you can decide to attack recklessly. Doing so gives you advantage on melee weapon attack rolls using Strength during this turn[...]

Note the emphasized text in each. Great Weapon Master is a choice made on each attack, while Reckless Attack is made before the first attack and applies to the whole turn.

So, you can turn GWM on or off for each attack. Say you roll a 18 on the die, then factor in whatever bonuses (ability score, proficiency, etc.) apply alongside the -5 from Great Weapon Master... and the DM tells you missed. You know that 18 is a good roll by itself, which means that the target has a very high AC. On further attacks in the same turn, you could choose not to suffer the penalty (and not to gain the damage) to increase your chances of hitting at all.

¹_{If you're going to roll all the attacks ahead of time for speed's sake, for fairness sake, you should declare if you're using GWM or not ahead of time. That way, you're not making a decision on information you don't actually have.}

You may use the +10 / -5 feature of the Great Weapon Master feat for each of your attacks. You do not add 20 or 30.

The fighter's extra attack feature mentions:

Beginning at 5th level, you can attack twice, instead of once, whenever you take the Attack action on your turn. The number of attacks increases to three when you reach 11th level in this class and to four when you reach 20th level in this class.

This means that you make multiple attacks whenever you take the Attack action.

The Great Weapon Master Feat mentions: (emphasis mine)

Before you make a melee attack with a heavy weapon that you are proficient with, you can choose to take a -5 penalty to the attack roll. If the attack hits, you add +10 to the attack's damage.

This in effect means that for each attack you make, you may choose to apply this Great Weapon Master feature, resulting in 20, 30 or 40 extra damage (in the case of a Fighter) in a round, but each attack has to be separate. This means that you may choose to apply it to some of your 2, 3 or 4 attack and some may not hit.

The text for Great Weapon Master just says

Before you make a melee attack....

There are no restrictions in the feat to how often you can do this on your turn, assuming you get multiple attacks per Attack action.

So, yes. You can choose to subtract 5 from every attack roll and do +10 damage on every successful hit.