From the rule you quote:
If either weapon has the thrown property...
Which weapon(s)?
a light melee weapon... [and] a different light melee weapon.
So the weapons of "either weapon" mention are the light melee weapons from the previous paragraph.
You can't throw both darts, because they're not valid weapons for two-weapon fighting.
And neither is a melee weapon, so:
You can't make improvised (dagger?) melee attacks with both.
But doesn't using a dart as an improvised dagger make it a melee weapon? "Improvised Weapons" (PHB p.147-148) says "in many cases, an improvised weapon is similar to an actual weapon and can be treated as such." (emphasis mine)
Nope. Later in "Improvised Weapons" we have "if a character uses a ranged weapon to make a melee attack...." (emphasis mine) The authors could have said "ranged weapon as a melee weapon" or something that indicated some change in the weapon's type, but they didn't.
It's still a ranged weapon, per the table, even when used to make a melee attack.
No, you can't take the -5/+10 while throwing a dagger.
Thrown: If a weapon has the thrown property, you can throw the weapon to make a ranged attack.
Throwing a dagger is a ranged weapon attack, so the first two benefits of the Sharpshooter feat will apply. However, the third benefit doesn't require a ranged weapon attack:
- Before you make an attack with a ranged 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 attackās damage.
It specifically requires that you attack with a ranged weapon. The thrown property doesn't change the fact that a dagger is a melee weapon. Throwing a dart, for example, would benefit from the -5/+10, because it's a ranged weapon. The thrown property isn't what's important here - what's important is whether the weapon is a ranged weapon or not.
If you prefer to hear it from the designers, Jeremy Crafowrd agrees that the first two benefits of Sharpshooter work with daggers, but not the 3rd. He also stated that a dagger is a melee weapon, even when you throw it, as well as including it in the official Sage Advice Compendium:
Does the Archery fighting style work with a melee
weapon that you throw?
No, the Archery feature benefits
ranged weapons. A melee weapon, such as a dagger or
handaxe, is still a melee weapon when you make a ranged
attack with it.
Best Answer
As Speedkat's answer mentions, almost1 all attacks are classified into one of four categories:
A ranged weapon attack is a specific kind of ranged attack. You can make ranged weapon attacks with ranged weapons (i.e. weapons on the Weapons table, listed as either simple ranged weapons or martial ranged weapons) - but you can also make them with any weapon that has the "thrown" weapon property:2
Basically, you can make ranged weapon attacks with weapons classified as ranged, or with weapons that have the "thrown" property (most of which are classified as melee weapons).3
If you have trouble understanding how melee weapons can be considered "ranged weapon attacks", read the term this way: it's a "ranged [weapon attack]", not a "[ranged weapon] attack". In other words, it's a ranged attack with a weapon, not an attack with a ranged weapon.
This is why the first two benefits of the Sharpshooter feat (PHB, p. 170) apply to attacks with thrown weapons, but the third benefit doesn't:
The first and second bullet points apply to all ranged weapon attacks - which includes both ranged weapons (such as crossbows) and thrown melee weapons (such as handaxes). However, the third benefit specifies "an attack with a ranged weapon"; as previously mentioned, thrown weapons are almost3 all classified in the Weapons table as melee weapons, so this benefit would not apply to them.
1 There are technically a few special attacks that aren't one of the four categories, but they're exceptions. The main ones everyone can do are grapples and shoves, which are both described as "special melee attacks".
2 You can also make a ranged attack with anything else you throw, using it as an improvised weapon:
3 The only weapons that have the Thrown property that are classified as ranged weapons instead of melee weapons are darts and nets.