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.