If she has an EF issue I think it would be apparent in areas outside of schoolwork. Does she need reminders about chores? Does she follow through with things that have nothing to do with school? Does she get her stuff together on her own...whatever she needs for school like lunch, gym shoes, books? If she is given an assignment that she enjoys, like say she is allowed to write about a favorite topic, or she can do a science fair project on any topic, does she do well in terms of planning and organizing the material on her own?
I think in school there are a certain number of assignments that a child can make as complex as they want. For instance, writing a personal essay. A fifth grader could write this at a high school level if they wanted. If she's not engaged at all even with those types of assignments, there is probably something else going on besides "boredom". KWIM?
If you have a school psych, they may be able to look into this without doing a full eval, for instance the BRIEF is an standardized rating scale for executive functioning. Worth a try to at least ask about it? In any event, I think you should sit down with the teacher and maybe the principal and share all of your concerns. There could also be something completely unrelated going on, like troubles with the other girls, and she doesn't want to talk about it.
