What do five year old girls like to play with? I asked her what she would like and she told me a big outdoor trampoline, an in-ground pool, and a play set. Sooooo... maybe not those things.
My oldest is
almost 8 and when she was that age, she loved doing just about anything outside: scavenger hunts, "helping" in the gardens, obstacle courses (I would set up things I could find around the yard or in the garage for her to climb over or under... the obstacles always seemed pretty stupid to me but she loved them). There is also a large private school campus near us with old buildings and gardens and trails that are open to the public and we would go there and she would wander around for hours (she particularly liked playing "spy" around the buildings. When we would go there, we would park in one spot and I would pack us a lunch and give her basically two or three destinations on the grounds that
I wanted to see and tell her to lead the way and let her take us on any route to get there. Basically, she just liked to explore. I have to imagine there's a park or some woods or a campus where you can do that near you too.
Other things she really enjoyed: Lego (though she needed a bit of help and would get frustrated easily until she was about 7 or so), My LIttle Pony (she absolutely loved them), arts & crafts (anything from coloring and painting or organized kits or randomly glueing weird sh!t together), helping in the kitchen (she still loves that), reading and comic books (she could spend hours in the library), play kitchen or restaurant with those fake plastic food stuff (she still loves this too). The local libraries are also often have a lot of fun classes and activities for kids that age too so be sure to check their schedules. And don't give the kids a choice, just say, "We're going to this African Drum troop or Dr. Seuss's birthday party or lecture on slimy slugs" or whatever the library is doing because in my experience she will always complain or say "no" when given the choice but end up enjoying it anyway.
She also discovered Harry Potter just after she turned 6. She was too young to read the books and my wife tried reading the first book to her but she just couldn't get into it. One day I decided to download the first book in the series on audiobook before we were going for a long drive to give us something new to listen to and she was absolutely hooked and I enjoyed listening to them with her too. The audiobooks are pretty long so it would take a while to get through them with listening in the car on longish drives or maybe for 30 minutes here and there around the house instead of turning on the TV. After we listened to the first couple of books my daughter decided she wanted to try and read them too so she started on the first book. It took her a few months to get through it but she eventually did and I think listening to the audiobook helped out, especially with strange words (particularly spells and strange names) that she had never seen before. Since then, she's read 5 of the 7 books and is nearly done with the 6th.
Even if Harry Potter isn't for her (or you), our daughter really enjoys audiobooks in general and I think they've helped her become a better reader and made her more curious about other stories/authors.
One last one that I just remembered: Home Depot usually has free or very cheap kids classes on Saturday mornings once or twice a month where you learn to build a birdhouse or something and my daughter always really enjoyed the ones that we went to.