Costume Quest and Costume Quest 2 would be something you could play together. The player character is the twin of your choice, a girl or a boy, on a mission to save their sibling. You would have to read it to her and probably solve the puzzles, but she would be able to do the fights once you got going since it is turn based. It's very kid friendly.
It's an older game but Beyond Good and Evil is a classic.
This wasn't mentioned and it's ideal: https://store.steampowered.com/app/1337010/Alba_A_Wildlife_Adventure/
Metroid dread
Some violence:
While stuff like Tomb Raider is the quintessential example, for a five year old you would probably be better with something more colourful and fun, even if you are the one playing it.
With that in mind my first thought was A Hat in Time although I've not played it through to verify end to end appropriateness.
You could also try Mirror's Edge because bright colours and dynamic movement, I don't remember it being that violent but maybe on second thoughts consider the safety aspect of introducing a child to the concept of jumping between buildings and maybe I'm talking myself out of this.
Celeste is colourful and fun and honestly at that age I don't know that she would pick up that much on the heavier aspects of the story which are allegories for anxiety/depression/gender dysphoria. A five year old is basically going to see it as a story with an evil twin I think.
I haven't played Child of Light but that might be appropriate?
The main character in Crypt of the Necrodancer is a girl called Cadence, although that is one you would really have to enjoy to make it worth it imo. I'm mostly thinking rhythm and bright colours are child friendly again to be honest, but you still have to play what is basically a roguelike mixed with a rhythm game and if that's not your jam it will be a waste of money.
You can always play a game with selectable skins too, like Spelunky 2 has a few characters you could pick between which all play the same but has a variety of designs you can play as.
Terraria has a bunch of options for gender PLUS it's the best game ever made.
Horizon: Zero Dawn would be an excellent choice.
New Pokemon Snap let's you choose your gender
How old is your daughter? This is important to know which games can be recommended and which games can't.
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Give Donut County a try.
Celeste! Pixel graphics, cute story, the bosses not too scary I think! Plus it’s very fun.
I'll split it into games your daughter could play, and some that could be fun to watch and get her to interact with. This is coming from someone who was playing Pinball 3D in preschool, so your mileage when bringing up a gaming child may vary.
One thing I haven't seen here is casual games. The less deep stuff that can still provide a lot of entertainment for kids that may just be starting to get a hang of things like computer mice and keyboard controls.
Alice Greenfingers (1 and 2) is a casual farm game featuring the titular character starting her own farm and selling the produce. No keyboard controls, just mouse controls and it was a pretty great introduction for me as a kid to finer motor movements.
The Diner Dash series is also a pretty good one to start. They have some variations, I know there's a detective game under the franchise that you could get input from your daughter on as you go through to encourage interaction.
There's the FATE (the WildTangent one, not the anime one) games, where it was one of the first games I remember that let me create my own female character. It's a diablo ripoff with much simpler mechanics. Gameplay can be repetitive but it's still a very fun, mouse-heavy game I still go back to. You can also choose between a cat and dog pet, and feed them special fish you find to turn them into awesome creatures like flaming unicorns!! (I'm sorry, I really love this game) i it's certainly playable with not much reading skill and therefore should be okay for a child, even if there's your standard combat violence.
For games that are fun to watch, I remember playing a Hello Kitty game for the PS2. There's still elements like hitting things, but it's overall a much cuter aesthetic.
There's also a PS2 Avatar: The Last Airbender video game that's based on the show (highly recommended watch even for kids), so you could relive the show you've just watched by playing the game with them. It's 2 player.
Crash Bandicoot Warped - while you play often as Crash, in the latest game I think it's possible to play everything as his sister Coco, who was already the only choice for some stages in the original game. Violence is mild, and was also one of my early games growing up. Fun to watch and play for kids.
I think there's a game called Infinity Nikki (PS4, PS5, PC, Android) that's a dress up platformer game. New outfits unlock different skills. The only issue is I've never played it, and it seems like microtransactions may inevitably come into play. Take caution. It's a crazy pretty game, though...
The Marvelous Miss Take (PC, and some consoles iirc) is a stealth game about a young woman trying to pull off several art heists. It features a female main character and is generally quite fun.
Hope this helps :)
I wish you guys all the fun!
Freedom planet series
La mulana 2 (though it has some adult jokes)
Undertale (frisk is deliberately gender neutral to be imprintable)
Touhou Luna Nights (the original touhou games too, though the translated dialogue doesn't always make sense).
I looked through most the comments and didn't see it, but Gris. Beautiful pastel color palette and a mount story about finding oneself / gaining your voice back. Very existential but in a passive way. I'd like to think of it as a Metroidvania, as you have powers to gain that open up new areas, but there's little to no actual fighting.
As a woman myself... i prefere a game where i can create my own pc and do my own choices. Cause i dislike the presentation of my gender in many games. But it is changing cause of society moving forward.
A game, for maybe in the future, cause it's still in early access: little witch in the woods
Immortal fenix rising has a female lead who is saving all of the greek gods
...
Profit
As someone who began playing video games around that age, I recommend Pokémon! She can pick her gendered avatar, then pick her favptite team of cute and/or cool creatures, and I'll swear up and down that my desire to embrace and understand that entirely text-based world of Pokémon nurtured my reading abilitiy far more than school ever did at that age.
Pokémon! It's like crack, but for reading, and also suitable for five year olds!
Portal (2) - Chell
I obviously haven't played it yet since it's not out yet, but I kickstarted "Girl Genius: Adventures in Castle Heterodyne" which is based on the Girl Genius comics. The comics are a bit violent and cheesecakey but the game looks like a more cartooney take on the story.
The "Girl Genius" setting is like a fantastical take on 19th-century Europe if it were run entirely by mad scientists - basically taking the Steampunk concept into more fantasy direction. The plot of the game: Agatha is a mad scientist with a heart of gold but she's also the lost last heir to the evil and depraved Heterodyne Family. To prove her claim to her birthright and save the city of Mechanicsburg she has to get the badly-damaged and utterly crazed AI-powered Castle Heterodyne under control.
The game is a puzzle-platformer.
https://store.steampowered.com/app/1789370/Girl_Genius_Adventures_In_Castle_Heterodyne/
Slime Rancher is a good one. It's bright, fun, has adorable critters and plenty to do and explore. There's a sequel too but I'm not sure if it's released yet or not.
The main character is a silent protagonist though so might not be completely what you're looking for
I don't have a game to add, but raising a daughter myself I'm taking notes on all these wonderful suggestions. (Actually I'll second the people who suggested The Hat in Time, hat kid is a character worth emulating lol)
Alba: A Wildlife Adventure You play as a young (7-ish years old?) girl exploring a Mediterranean island, taking pictures of cute animals and saving a nature reserve. Very child-appropriate and a joy to play. Highly recommended!
Here's a list of game's I'd highly recommend from across all of space and time, filtered on female lead, and excluding ones where you can choose or design your own character), edit: filtered for most egregious age 5-inappropriate, random order:
Risk of Rain 2? If I recall right, most characters are female or ambiguous. Noita is another flawless gem.
Are games where gender isn't explicitly defined okay?
Super Mario bros 2 you can play as princess peach. The game is of course not trivial to play.
A Hat in Time
Some of these might be a little more like 8 than 5 because they have storybook-scary but still mentioning for you to have a look and decide.
Lost Words - Beyond the Page
Unpacking
Epistory - Typing Chronicles
One Step from Eden
Wargroove
Tsioque
Technically not female lead but kinda close and definitely age-appropriate:
Chicory - From creators on Wandersong + Celeste. Not positive your character is canonically female but let's just call it very plausible and you are filling in for the titular character who is called "she".
Donut County (technically the male racoon is the main character but the only human and next-most important character is female)
Journey (likely canonically no specific gender but great game, no dialog and could easily interpret as female if you choose)
Not what you asked for but maybe consider:
Beglitched - No human characters other than the player, puzzle game with pink and purple hacker aesthetic.
Lovers in a Dangerous Spacetime - Androgynous animals and humans pilot a wacky ship in 4 player co-op lots of hearts.
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