RetroGaming

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

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.

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

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.

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

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.

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.

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.

"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.

Battle City

Super Mario World, Battletoads

Goof Troop, for SNES.

Super Mario by far IMO, basically all of the games.

5yo is probably still too young to understand Zelda.

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)

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

Turtles in time

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

Mortal Kombat is pretty tame I hear.

( ͡° ͜ʖ ͡°)

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! Let the 5yo be tails! He'll never die. He can collect rings and kill enemies. It's the best 2 player platformer ever created

Magical Quest 2 & 3 are very good for that. They already know the characters, and the games are beautiful and pretty good gameplay-wise.

You play together and if the child loses all his/her lives, he/she can steal yours. For difficult sections or bosses, you can do it alone.

There are new costumes regularly so the child wants to continue to discover the next costume, and its associated powers.

Magical Quest 2 is easier than 3, so I think it’s better to start with this one. You can either play as Mickey or Minnie.

In Magical Quest 3, you can either play as Mickey or Donald. Donald is meant to be played by the child because his gameplay is a bit different (with his soldier costume which is wooden barrel, preventing him to sink while Mickey has a silver armor which kills him if he goes into water with it). It’s not that difficult to play as Mickey (my nephew did not want to play as Donald and we had no major issues).

The NES sesame Street games are pretty good.

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

World of Illusion (Genesis)

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

On the SNES, all of the games below have coop:

• Tiny Toons Wild and Wacky Sports - a collection of several silly minigames as some sort of tournament, with minimum scores that need to be reached. No direct violence between players, only cartoon shenanigans like falling down a cliff, snowballing after tripping while skiing, etc. (Maybe show the kid some of the old cartoons as well, if s/he enjoys, I'm sure the game will be more interesting to him/her)
• Super Bomberman - Might count as "violent", since you're bombing weird looking enemies, but it's a formula that rarely gets old and plays great as co-op. Your kid might enjoy 3 and 4 the most, with the variety of mounts to be had (if your rpi can run NeoGeo games, Neo Bomberman is also a great choice)
• Top Gear - Racing game with one of the best soundtracks in the console. Top Gear 3000 goes to space and has plenty of options for upgrading your car.
• Secret of Mana - Might count as "violent", especially as you start off with a sword and kill cute bunny-thing enemies. An action RPG that, once you get the 2nd character, it can be played with the 2nd controller. Drop-in/drop-out, so you can easily join and leave while your kid plays or vice versa. The same applies for Secret of Mana 2 (Seiken Densetsu 3)
• Magical Quest 2 and 3 - Disney games that are best when played cooperatively (the first lacks coop). Starts off easy enough and you get new costumes that give special powers, which help you out in the stages going forward. It's "Disney violence" how you beat most enemies (jumping on their heads, spinning them against one another)
• Kirby Super Star and Dreamland 3 - Both allow for a second player to join in and help. Dreamland 3 has a very unique and cute looking style.
• International Super Star Soccer - If you're into normal football (soccer), this is easily the best of its kind for the 16-bit era
• NBA Jam - Also available on the Mega Drive, dunno which version is better. BOOM SHAKA LAKA!!

My kid used to love one of the Kirby games for the Wii, where the three of us could play at the same time. I can't remember the name of it, but I'm pretty sure it was previously released for the SNES. It was the one with Armor Knight, if I'm remembering the character name correctly.

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

City Connection, Bugs Bunny's Crazy Castle. While neither are co-op my mom and took turns playing crazy castle on the nes when I was a kid and we beat it. Core memory right there.

I think Tetris or Doctor Mario had 2 player modes but I'm not sure.

Does Sonic Spinball on the Genesis have multiplayer?

Oh, and sorry for so many responses, but I figure that posting these separately will let the votes give you some idea where to start.

The votes I've seen so far very much reflect the order I would try these games out with a five year old gamer.