My daughter was about 4 when my mom got her two granddaughters the bitty baby twins. They each got one, and they are little smaller so not as expensive as the full-size dolls. It was good for a trial.
She didn't ask for it--my niece (age 7 at the time) asked for the AG doll and my mom got them for both girls anyway. Honestly, she didn't play with it much at 4, but as the years went on, she started asking for the full size dolls and now has two of them also. (Thanks Mom--I probably wouldn't spend that much on a doll myself!)
Now, at age 10, she is obsessed. Her room is set up for her dolls and their stuff. I'm glad because they were expensive and she is now finally playing with them! The nice thing about the AG dolls is that because they are marketed for older girls, they won't outgrow them so fast.
Anyway, if your daughter is ASKING for one at 5, she is probably ready, and probably does plan to play with it. I didn't have any trouble with my daughter mistreating the doll at age 4. She cut her Barbies' hair, but knew not to do that to the AG dolls.