As usual, having less classes or races to choose from does not make for a "simpler" game, so it's the wrong question to ask.
To have an even simpler game than 5e already is compared to other editions, you'd rather simplify the mechanics of combat and non-combat resolutions, for example by:
- removing action economy: have anything that's not moving be a simple "action", and a turn be just action+move
- removing all game-specific actions of the combat chapter other than attack, cast, and use an object; let the DM allow anything else reasonable as an action
- replacing all death and dying rules with "you die if you fall below 0 hp" or let the DM decide what happens
- removing the weapons and armor lists, having a fixed damage for all weapons and a fixed AC for all armors
- removing all rules for cover, visibility, searching, jumping... removing literally ANYTHING that determines or modify resolutions, except the generic ability score rolls and dis/advantage, and let the DM decide each situation
- removing all spell components
But to play along, you could try to select the 5 classes that seem to have the lowest complexity both in terms of less choices to make and simplest rules for their abilities, and attach the one subclass that similarly seems to be of lowest complexity. Then simplify even more if possible. I don't really think it matters to have 5 or 12 classes, that complicates choices at character creation, but if you intend to play a campaign then it won't make a difference after all players made their choice at level 1 (because you are not going to allow multiclassing in a theoretical exercise about simplifying the game, or you've already lost). And I don't think there are classes with enormous, non-debatable differences in complexity: one can argue that Sorcerer is easier than Wizard because it doesn't have to choose the daily list of spells, another that Wizard is easier than Sorcerer because it doesn't have to consider using sorcery points or metamagic. Maybe consider having a new spellcasting class that has neither of those features, instead of either Wizard or Sorcerer. In fact, that's what I would probably do:
Warrior,
Priest,
Burglar and
Mage, each of which possibly merging concepts from multiple classes by
removal of abilities (if you're worried about characters getting weak, replace removed abilities with stat bonuses).
For races, just remove all mechanics and let players choose whatever creature they want for cosmetic reasons.