I recommend saying that the school decided that she should be in fifth grade (this statement is true, because even though you advocated, it wouldn't have happened if the school hadn't made the decision; people don't have a right to know all the details).
This statement is neutral and puts the responsibility for the decision in the school's hands and keeps your daughter out of it. Kids are used to being told what to do by the school, and if she frames the decision this way, it sends a message to other kids that she's still just doing what they told her to do, like everyone else. This approach may reduce resentment ("she thinks she's so big!"). If anyone asks why (a reasonable question), she can tell them that the school made her take some tests. Again, not her choice, and again, she's just doing what kids do every day.
