Sixth if you include Basic.
Well... seventh if you include OD&D...
WoTC has only done 3 though the current design group 2.
Ironically in the lead up to 5E when I was designing my own D&D/playing retroclones I think I did solve the problem of high level play. I revised my homebrew once 5E landed. Here is what you need to doIMHO to make D&D work at higher levels.
1. Build you D&D around the only D&D to halfway function well at higher levels. That is BECMI.
2. Use modern mechanics, d20's, ascending ACs probably 5E skill and proficiency system.
3. Don't use feats or if you do have them low powered. In 5E terms alert and mobility are the best ones.
4. Use AD&D concepts for the monsters picking up where 2E left off. This means a Dragon for example is similar to 5E ones but has AD&D breath weapons, spellcasting a'la 3.5, and AD&D magic resistance.
5. Use gritty hp recovery per day, the 5E one doesn't cut it even the variant rules. By gritty I mean 1d3 hit points per day or perhaps 5E HD system but you only get a single HD back per day.
6. Dump bonus action and short rest mechanics.
7. Use the BECMI/C&C/ACKs atributes (1-5 +1, 16-17 +2, 18+3)
You need a lower powered game with more resilient monsters with a less generous HP recovery.
I also would argue that you use the old xp system as well so Rogues for example level up faster, and I would also overhaul the saves. ZYou would also have to tone down the gonzo levels of daamge 5E monsters deal.
Some example
Kobold CR 1/8
Small Humanoid LE
Initiative +2 Senses Perception -1 darkvision 60'
HD 1d6-1 Hp 3
AC 12
Abilities Str 8 Dex 14 Con 9 Int 9 Wis 8 Cha 10
Saves Fortitude +1, Reflex +4 Will +1
Speed 30'
Attack Melee +4 Dagger Dmg 1d4-1 or
Ranged +4 Sling Dmg 1d4
SQ: Shifty, Trap Sense The Kobold gains a +2 bonus to all defenses against traps.
Alignment Lawful Evil Languages Common, Draconic
Skills Stealth+4, Thievery +4
Equipment 3 javelins
Traits
Shifty (bonus action ) The Kobold moves 5’ and doesn’t provoke attacks of opportunity. .
Light Sensitivity: While in sunlight, the kobold has disadvantage on attack rolls.
Ogre CR 1
Large Giant
Initiative -1 Senses darkvision 60'
HD 4d10+8 hp 38
AC 12
Saves: Fortitude +6 Reflex +2 Will +-1
Speed 40'
Alignment CE Languages Giant
Skills Perception +3 Stealth +10,
Str 18 Dex 8 Con 18 Int 5 Wis 7 Cha 7
Skills: Athletics +6
Equipment: hide armor, club, 3 javelins
Actions
Attack: Melee +6 Dmg 2d8+4 (club)) or
+6 ranged damage 2d8+4 (javelin)
Another easier option would be something like revising C&C and adding in things from 5E you like and fixing some of the odd things in that system.