Eilistraee is alive and kicking in 5e D&D/FR. She has returned during the event known as the Sundering. It is also very well possible that she didn’t die at all, for a lot of reasons:

At some point Liriel was. At the end she chose to be a cleric of Mystra, as she thought that she could have never have a place among worshippers of Eilistraee because of all the deaths that she -unwillingly- brought upon them. However Eilistraee never turned her away and she could still hear the goddess’ song calling…

Don’t worry, Eilistraee’s alive and kicking in 5e. Ed Greenwood confirmed it (http://forum.candlekeep.com/topic.asp?TOPI…) and mentioned her in his novel ‘’Spellstorm’’ as one of the deities with whom Mystra is currently sharing the Weave.

Drow in FR are not evil by default. Many of them are, but the race isn’t like the GH one. Currently, in 5th edition, even the PHB states that they can choose and, since Eilistraee is officially alive in 5e D&D/FR, those of them venturing to the surface are likely to pray to her among other gods.

Eilistraee is awesome! She was one of the main things I missed in 4th edition Forgotten Realms. I hadn’t even read the Drizzt books, but I think it’s a strong instinct in a lot of players to take a race that’s “all evil” and play one against type, because having a sentient race being “all” anything is a lot more…

In the second expansion for the Atari-remade Neverwinter Nights, Hordes of the Underdark, the player meets up with a camp of Eilistraee’s worshippers. They play a fairly significant role in the second Act.

Eh, there’s a few mentions throughout the books, but overall Drizz’t doesn’t do much with Mielikki; I stopped reading the series after the orc trilogy but I recall he had a pretty big faith moment in the first or second book of that trilogy. I’d point out that Elistraee actually got started with another drow character…