+1. Seems a bit early to me. Let her be a kid. Especially let her participate in other sports if she shows an interest in them. Let her play soccer, or lax, or hoops - whatever. All of them involve running and in the long run they will make her a better all around athlete. I would also say that a 5th grader should never race in anything more than a mile or two mile, preferrably on a track and not road races.. No 5K road races or any of that stuff. Too much stress on a young body. Stress of too much, too early can really be damaging, especially for young girls who tend to put more internal stress on themselves than boys. Another suggestion - keep an eye on her weight. too many young girl runners have serious issues with anorexia and bilomia. Having a few extra lb's is not a big deal.
Just my 2 cents.