RetroGaming

Lode Runner (NES) might be okay. Not multiplayer, but it's got nice low-stakes puzzling gameplay.

Edutainment games are a bit few and far between on consoles - Donkey Kong Jr. Math springs to mind, but it's remarkably dry for a Nintendo game.

Troddlers - SNES

The music in Troddlers slaps.

Its a puzzle platformer game similar to Lemmings. Little dudes walk in a straight line and you play as a wizard that can place blocks. You have to get the little dudes to the exit.

The only violence is when the little guys or the other player gets smooshed by a block I think, its been a long time since I played the game.

Pacman! I am not entirely sure, but I think it was an Atari 2600 where I really enjoyed this on at a similar age

SNES:

• Harvest Moon - this can lead into allowing the kid to plant something IRL and having them water it regularly, allowing them to "be a real farmer". Incidentally this is also a great way to get a child to eat vegetables, as a child who refuses to even consider eating a vegetable will change their mind when they grew it themselves

• Super Mario Kart

Mega Drive:

• Dr Robotnik's Mean Bean Machine - simple puzzle game with humorous characters from the old cartoon

R.C. Pro Am

The NES sesame Street games are pretty good.

My youngest loved sesame Street countdown. it was really forgiving and taught her basic platformer mechanics.

Lemmings for Amiga had a 2player split screen mode. Goal is to guide the most lemmings (yours and the other players) into your exit.

A bunch of arcade games become much more friendly to kids with infinite continues, shmups, fighters, brawlers, etc but for those you'll need to filter on violence. I'd probably also avoid anything RPG or story heavy.

My picks would be Bubble bobble, Kirby on SNES, ice hockey on NES, Mario 1-3, super Mario kart, Tetris, monkey ball, Dr Mario. For Sega Sonic 1-3 & knuckles, ecco, robotnik's mean bean machine, Alex kidd, outrun

It doesn't count as non-violent, but every kid I have played it with has thoroughly enjoyed the TMNT arcade game (as well as the Simpsons game that plays similarly. If you play with them you can essentially carry them through the game and they are just along for the ride, but feel like they are part of the team.

Joust. Easily understood game for little ones, and you can discourage player killing.

That's easy. Daggerfall.

A c64 emulator? Then basically anything, LOCO maybe?

Kirby Super Star

Bubble Bobble is one of my favourite retro multiplayer games since it has both players playing simultaneously (not each take a turn/hand off the controller) but might still be a bit difficult for a 5 year old 🤔

Edit: Tetris & Dr. Mario for the SNES might also work

Lots of other great suggestions. But I do think the consensus is multiplayer games with coop.

Konami beat ‘em ups like TMNT, The Simpson, Xmen would be great.

I’m also going to throw in Party games or kart racers, CTR and Mario Kart of Mario Party or Crash Bash would also be great

That said Pokémon might be a nice option too though not sure how you’d play that together.

Or edutainment like Gizmos and Gadgets or Jumpstart

Sonic 2. Make him be tails. As is tradition.

Sonic 2.

Controlling Tails can be good fun if you’re very young and don’t fully know what you’re doing!

Can be hard keeping both characters on screen at times though.

Hard to beat Super Mario Brothers. I tried other classics, bunch of arcade games, but my son never liked them. Ms. Pac-Man might work. The big hit with us was Wii sports.

TMNT Turtles in Time on SNES. Its a fun game and kids can button mash, and turtles are still relevant today. Puzzle games like tetris can be good for using the brain. There were a ton of puzzle games in the snes era, like bust a move (puzzle bobble), yoshi's cookie, puyo puyo (kirby's avalanche), and many more.

I would mostly avoid NES because it looks really dated, aside from a handful of the real classics like Super Mario Bros 1 & 3.

Super Mario World, Battletoads

Kirby Superstar (SNES) is great for this, I play it with my 5-year-old. The second player plays as the "helper" character, and when they die, Kirby can create them again. It effectively plays like a "buddy mode." That game is also one of my all-time favorites just for what it is, so I'm a bit biased.

Pong

You both can play Goof Troop. It's a Co-op game with Goofy and Max as protagonists, it's very funny.

"Toejam and Earl: Panic on Funkotron" (Genesis) has a very well designed "little kid mode" in the options, and it's still really fun.

Edit: Example regarding violence - you get to throw jars at humans to trap them for transport back to earth. And you need to watch out for bowling balls falling out of trees.

Goof Troop, for SNES.

Balloon Fight (NES)

from a sega childhood my top:

• toejam and earl
• micro machines
• world of illusion (mickey and donald)
• California games
• Bonanza Brothers (has guns but in game they are tranquilizers and enemies wake up)

Sonic the Hedgehog 2. Little one can be Tails and play coop.

I would say that most retro games can be enjoyed by a 5-year-old (having once upon a time been a 5-year-old playing some of them myself), but the first one that comes to mind is Donkey Kong Country.