|Image from the 5e PHB|
In fact, there are so many options it can be daunting to keep track of it all, and remember what thing is in which book. If I've missed something, let me know on G+ and I'll add it. I'll try to keep these updated as new stuff rolls out.
I've made some tables to help:
5e D&D Races
5e D&D Classes and Class Options
(1) That said, I would probably allow it if a player asked nicely and the option in question didn't look like janked-up nonsense.
(2) Also, I wouldn't mind if we got some good content from Eberron ported over to 5e. And I look forward to seeing the finalized mystic and artificers.