Im a single dad on the Arctic Coast, I take my kids out every chance wx permits, even bring there friends along with there folk's permission, fishing & swimmin, plinking
When his 8yro he can join 4-H they have shooting in a structured environment and they make life long friends.
I'd say transparency and communication is crutial and pay particular attention to personal safety, one slip of a pocket knife and stiches would be all she wrote to end your outdoors fun, a 5yro is old enuf to do tons of stuff, not involving firearms at first, wood craft, tracking, nature hikes, photography, name the grasses,trees (pressing flowers & leaves), ID'ing animals (have sence enuff not to pick up critter babies, rabbits, squirrels, skunks& raccon), what plants are edible and when & what parts are edible, handling turtles, lizards, toads, bugs, shooting a bow & arrow, rock hounding is another (had GF turn the kids onto looking for heart shaped rocks and rock tumbling), the diffrent birds, riding a poney (trail ride weekends?), learning to swim, raft, canoe, safely climbing trees,building bird houses (nail up in Woods) building a camp, building a camp fire (like 8yro and up), stressing safety all the way, its a trust issue, kids do get hurt learning to do stuff its gonna happen she's gotta be aware that may happen.
I was 8yro when I got a daisy Red Rider BB gun, I was 9 I got a Crossman Pump, 11 a .22 single shot of my own, 16 a 12ga shotgun, of course I grew up rural and my folks were and still are married, the emotinal distance is a tough one to deal with as your not going to get much sympathy for her.