Playable Gith in 5e?

Githyanki AD&D
+1 Dexterity, +1 Intelligence, -1 Wisdom, -1 Charisma
Racial Maximums of 19 Dex and Int
Class Restrictions: Fighter, Mage, Gish (Fighter/Mage), Psionicist
Astral Movement rate of 96
Double odds of having psionic wild talents
Malign Reputation: -2 reaction penalty with Good NPCs, -1 reaction penalty with Neutral NPCs
Racial Enmity: Githzerai: -8 reaction penalty with Githzerai, stacks with Malign Reputation
The Lich-Queen Is Watching: Upon hitting 11th level, the PC has Vlaakith CLVII's attention; if they reach 12th level, she senses it and will dispatch several waves of githyanki "retrieval teams", then turn to local resources (assassins, etc), not stopping until either she or the githyanki character is dead. Githyanki can choose to deliberately not gain any levels after 11th to avoid her wrath.

Githzerai AD&D
+1 Intelligence, +1 Dexterity, -1 Strength, -1 Wisdom (PO:S&P instead presents them as having no racial ability adjustments)
Infravision 60 feet
Alignment Restriction: Cannot be Lawful
Class & Level Limits: Fighter (9), Wizard (12), Thief (15), Zerth [Fighter/Mage] (9/12)
Magic Resistance: Githzerai Fighters and Thieves have Magic Resistance 5% per level (maximum 95%); this power cannot be suppressed, and the first time a githzerai attempts to use an item, make a Magic Resistance check; if succeeded, then that item's magic will never function for that githzerai as a result. Githzerai wizards do not have magic resistance, and fighter/wizards must choose whether or not they have it.

Githyanki 3.5
+2 Dexterity, +2 Constitution, -2 Wisdom
Medium
Base Land Speed 30 feet
Darkvision 60 feet
Naturally Psionic: Increase your Psionic Points Pool by +3 psi points.
Psi-Like Abilities: At 1st level, you can use the Psi-Like Abilities of Far Hand and Psionic Daze 3/day each. You also gain the Psi-Like Abilities of Concealing Amorpha (3/day) at 3rd level, Psionic Dimension Door (3/day) at 6th level, before finishing with Telekinetic Thrust (3/day) and Psionic Plane Shift (1/day) at 9th level.
Power Resistance: Hit Dice + 5
Favored Class: Fighter
Level Adjustment: +2

Githzerai 3.5
+6 Dexterity, +2 Wisdom, -2 Intelligence
Medium
Base Land Speed 30 feet
Darkvision 60 feet
Naturally Psionic: Increase Psionic Power Points Pool by +2 Psi Points.
Psi-Like Abilities: A githzerai can use the psi-like abilities of Inertial Armor, Psionic Daze, Catfall and Concussion, all 3/day. At 11th level, they can also use Psionic Plane Shift 1/day. Manifester level is equal to 1/2 Hit Dice (minimum 1st) and save DCs are Charisma based.
Power Resistance: Hit Dice +5
Favored Class: Monk
Level Adjustment: +2

Githyanki 4e
Ability Scores: +2 Constitution, +2 Intelligence
Size: Medium
Speed: 6 squares
Vision: Normal
Skill Bonuses: +2 History
Danger Sense: +2 bonus to Initiative checks.
Githyanki Willpower: +1 to Will defense, +2 to saving throws against Charm effects.
Racial Power - Telekinetic Leap: Usable 1/Encounter, Move Action, target Self or 1 ally within 10 squares. The target of this power can Fly up to 5 squares; if you use this on an ally, that ally must remain in your line of sight at all times during the effect.

Githzerai 4e
Ability Scores: +2 Dexterity or Intelligence, +2 Wisdom
Size: Medium
Speed: 6 Squares
Vision: Normal
Skill Bonuses: +2 Acrobatics, +2 Athletics
Danger Sense: +2 to Initiative checks.
Shifting Fortune: When you use your Second Wind, you can shift 3 squares as a free action.
Racial Power - Iron Mind: Usable 1/encounter, when you would be hit by an attack, you can increase all of your defenses by +2 until the end of your next turn as an Immediate Interrupt.

For Githyanki, let's see... we started as a Dex/Int boosting race, then a Dex/Con, then finally a Con/Int race. So that makes the ability scores hard to decide upon. One could always go with just giving them +1 to all of those stats, but isn't +1 in three stats usually considered inferior to the +2/+1 split approach?

If you look at their two more recent statblocks, there's a certain focus on mobility. 3.5 gave them Dimension Door and Planeshift spell-like abilities, 4e gave them Telekinetic Leap, and 5e gives the monster versions Jump, Misty Step and, for Knights, Plane Shift SLAs. So that's definitely something worthy to preserve. Heck, even back in AD&D, their monstrous incarnations could Plane Shift at will, an ability too potent to give PCs of course, but which emphasizes that githyanki should be capable of unearthly mobility.

Telekinetic abilities, to support their psionic nature, are also a feature in both 3e and 5e.

Not directly referenced in their statblocks, but githyanki are heavily associated with combat (hence the Fighter favored class in 3e), arcane magic use (they invented the term "gish" we still use today for martial/caster mixed characters), and the use of greatswords, which are their most iconic weapon, as iconic as the dwarf with his axe and his hammers.

It has no tradition, but I really like the 4e version's Danger Sense and, especially, its Githyanki Willpower trait - the githyanki are culturally defined by their obsession with freedom and their hatred of the illithid, who rely heavily on Charm effects. It makes sense, doesn't it, that githyanki would be resistant to effects by others to sway their minds?

With a Githzerai, I think everyone immediately leaps to "+2 Wis, +1 Dex" as their ability score modifiers. Despite their Dex/Int origins in AD&D, they've become so iconically associated with monks and sages that it's hard to think of otherwise - I really liked 4e's version for giving us Dex or Int as the "flexible" racial modifier, since it actually harkens back to their tradition of training Zerths - warrior-wizards - as stand-ins for priests of Zerthimon. Alas, we can't do fluid ability modifiers anymore.

Looking at githzerai across the editions, you'll notice that their recurring theme is, surprisingly, mentally-bestowed toughness. They had Magic Resistance back in AD&D, when magic was king, they had Inertial Armor as a psi-like ability in 3rd edition, and they had Iron Mind as their racial power in 4th edition. Even in 5e, their "Psychic Defense" trait and Mage Armor SLA means that githzerai are surprisingly tough foes despite rejecting armor, which is itself a reference to their monkly aspects.

Mobility's another recurring theme; Catfall as a psi-like ability in 3.5, Shifting Fortune in 4e, and access to Feather Fall and Jump SLAs in 5e. Again, this fits into githzerai and their strong post-AD&D association with the Monk class. They're the iconic kung-fu arsewhuppers of D&D.

Putting all that together... now that's the tricky part...

>>55207782
Githyanki
Ability Score Modifiers: +2 Dexterity, +1 Intelligence
Size: Medium
Speed: 30 feet
Vision: Normal
Blades of Gith: You have Proficiency in the Greatsword. When making melee attacks with a Greatsword, you can use your Intelligence modifier to determine your damage modifier.
Mind over Matter: You can cast the Mage Hand cantrip, although your version is invisible. Additionally, you always count as having a running start when making Jump checks.
Hate Breaks All Shackles: You have Advantage on saving throws against the Charmed and Stunned effects, and on saving throws to end those effects.

>>55207802
Githzerai
Ability Score Modifiers: +2 Wisdom, +1 Dexterity
Size: Medium
Speed: 30 feet
Vision: Normal
Graceful As Thought: When you Dash, you can ignore the effects of non-magical difficult terrain. You also have Advantage on Acrobatics checks.
Inertia Armor: When not wearing armor, your AC is 13 + your Wisdom modifier. You can use your natural armor to determine your AC if the armor you wear would leave you with a lower AC. A shield's benefits apply as normal while you use your natural armor.
The Knowing of Self: You have Advantage on saving throws against the Charmed and Stunned effects, and on saving throws to end those effects.

>>55207873
This versions favors Dexterity and Intelligence because the githyanki are traditionally described as extremely quick and agile (high Dex), but also intelligent and adept at arcana (Int). It also reflects their tradition of training wizards and the special place they hold in githyanki society.

Blades of Gith not only grants them an iconic weapon proficiency, but allows them to still use those weapons to lethal effect despite their not otherwise making particularly great fighters (the 5e MM's depiction of Strength as their highest value is quite uncharacteristic).

Mind Over Matter gives the player a relatively balanced access to their traditional telekinesis, and its jumping bonus references Telekinetic Leap, itself a more player-friendlyform of enhanced mobility compared to the traditional dimension doors and plane shifts.

Resistance to Charm and Stun gives the githyanki a great advantage when hunting its traditional enemy, the Illithid, which uses both conditions to subdue PCs.

Honestly... I think this looks flavorful, but maybe a little overpowered. I considered giving it Arcana proficiency (to represent their extensive anti-illithid training) and/or the ability to use Incorporeal Movement, but I worried that those would come off as too overpowered or uncharacteristic.

>>55207894
This version struggled to make itself work; 5e doesn't use the same kind of dynamic combat that 4e did, so fluidity is hard to pull off. Still, I rather like Graceful As Thought, which makes githzerai naturally mobile without treading too heavily on the monk's toes.

Inertia Armor is literally just the Lizardfolk's Natural Armor using Wisdom instead of Constitution, but hey, why reinvent the wheel?

The Knowing of Self... yeah, I was actually conflicted on whether or not to add that, but since githzerai are just as militantly anti-illithid as the githyanki, just with different ways of training against them, I felt it was a viable way to highlight that shared connection.