I'm just starting out with D&D, and while I haven't played yet, I'm in love with all the things in the PHB. But I am a sucker for self-torture/more content, and I was wondering what got left behind when 5e came out in terms of playable races.

What playable races were cut in the transition from 4e to 5e?

This is an interesting question that could be rephrased as "What's not in 5th edition...yet?" because Wizards has indeed been filling in some of the gaps.

To start with, though, 4th Edition had much more source material... velocity(?) than 5th. (This is intended, as I understand it). Races are actually one of the easier things though!

At its start, 5th edition lacked:

(A * denotes that the race in question has been combined or altered, or is otherwise inconclusive as to whether or not it was truly "carried over" between editions)

Player's Handbook

• Eladrin* (Now an official Elf Subrace as of MToF)

Interesting to note that Half-Orcs and gnomes did not make it into this book (they're in PHB 2 instead), but PHB to PHB, the initial races available were otherwise nearly the same.

Player's Handbook 2

• Deva* (Parallels with Aasimar from VGtM)


• Longtooth Shifter


• Razortooth Shifter


• Goliath (Added to 5e w/ VGtM)

4th edition didn't have nearly as many subraces as 5th does, but Shifters (a lycanthrope-blooded race) got two.

Player's Handbook 3

• Githzerai (added to 5e w/ MToF)


• Minotaur (does the Ravnica supplement count for 5e here?)


• Shardmind


• Wilden

As an interesting note, 4th edition didn't let you do organized play as a Githyanki, only a Githzerai. Shardminds were psionic crystal beings with a sort of hive consciousness if I remember correctly, and Wilden were plant people who had "seasonal" subraces they could change between. (5e Eladrin picked up some of that, actually)

Dragon Magazine

• Gnoll


• Shadar-kai* (Now an official Elf Subrace as of MToF)

In addition to the books, 4th edition's monthly Dragon magazine added 2 official races. Interesting to note here that 4e Shadar-kai weren't elves.

Monster Manuals

• Bugbear (Added to 5e w/ VGtM)


• Bullywug


• Duergar* (Now an official Dwarf Subrace as of SCAG)


• Hobgoblin (Added to 5e w/ VGtM)


• Kenku (Added to 5e w/ VGtM)


• Orc (Added to 5e w/ VGtM)

These races had minimal "official" support, but stats / powers / etc. were provided for these all the same.

Finally, there were a number of singular or campaign-specific races that showed up in other random sources

Misc

• Kobolds (Added to 5e w/ VGtM)


• Svirfneblin (Now an official Gnome Subrace as of SCAG)


• Goblin (Added to 5e w/ VGtM)


• Bladeling


• Changeling


• Genasi (Added to 5e w/ EE)


• Kalashtar


• Mul (Half-Dwarf)


• Revenant


• Shade


• Thri-kreen


• Vryloka


• Warforged


• Hamadryad


• Pixie


• Satyr

Fun fact: Drow weren't in the Player's Handbook in 4th edition! To play them you'd have to wait 3 months past 4E's debut. Genasi show up here with 13(!) subraces. Shades are like the Shadar-kai in that they were humans who lived in the Shadowfell, but I'm murky on how precisely they were different. Vrylocka are vampire-folk.

Conclusion

First, I'd be remiss if I didn't add a disclaimer that I may have missed one (or more!), so think of this as a thorough, if not comprehensive, comparison.

All together, it looks like 27-33 races were "lost" in the transition, with a smaller number of 16 that have no representation as playable races in 5e as of this post.

Missing from 5E

• Longtooth Shifter


• Razortooth Shifter


• Shardmind


• Wilden


• Bladeling


• Changeling


• Kalashtar


• Mul (Half-Dwarf)


• Revenant


• Shade


• Thri-kreen


• Vryloka


• Warforged


• Hamadryad


• Pixie


• Satyr

Some of these races (Kalashtar, Changelings, Warforged, Mul, and Thri-kreen) are campaign specific to either Eberron or Dark Sun so might be expected in the future, but the rest of this list is probably unlikely to be seen soon (if at all).