Respectfully, I don't necessarily think that the right answer lies with "stats", because stats can say something like that 99 percent of kids do "x", but your daughter may be the 1 percent that won't do "x".
I think it's a matter of being truly open to assessing what a little kid wants, how enthusiastic she is, or whether she's kind of neutral but thinks it sounds like a good idea - mostly because most little kids think everything new sounds like a good idea.
There are parents who say they won't let their child quit anything. I don't think that's good if a child tries something and discovers she doesn't like it.
As with so many things in life that involve children, I think letting your child be the guide offers the best chance that she won't be at high risk of burning out from anything; because burn-out most often happens not because someone is kept busy or challenged with a lot of an activity, but because he spends too much time at an activity that isn't really something he's enthusiastic about - or worse, hates.
I have three kids now grown. My sons were involved in different sports but also other activities, but they didn't start as young as five because, for the most part, that wasn't the age little boys were starting baseball in our area.
My daughter, on the the other, was three when she wanted desperately to go to kindergarten. If the school hadn't changed the age to "full five" I would have only had to stall her off until she was about to turn five. Instead, she had to wait another whole year; and throughout her whole school "career" she always felt just a little older than the other kids and was never quite as challenged as she would have liked.
Same daughter: Started dancing school at three and loved it. She's twenty-eight today, working full-time, has a little business of her own, and has all kinds of other things keeping her busy; and she still makes sure she gets to dance with a "community/arts" dance company.
On the other hand, she tried T-ball at four or five, liked it OK, and decided she didn't want more baseball. She asked for violin lessons as well.
I really believe that letting your child and your own common sense and understanding of her - not stats - be your guide is what will most likely reduce or eliminate the chances that she'd burn out. When the "enthusiasm light" gets extinguished in a child's activities it's pretty easy to notice that. My own feeling is that that happens long before any burn out might.