Of course it would have been unheard of when I was in 5th grade because our assignments weren't even computer readable. In my day, we were expected to copy articles from the World Book Encyclopedia, and they were graded on neatness.
But my kids both recently graduated from high school. There is a tendency for teachers of each grade to prepare kids for subsequent grades. I can imagine hearing: "They will have to do this in sixth grade, so we're preparing them now" without questioning why it's done in any grade. This makes the curriculum seem more "advanced."
I actually don't think my kids had to use turnitin. At least, I never heard about it. A bigger concern is writing stuff that might be reviewed by employers, law enforcement, and so forth, or subjected to some kind of automated analysis in the future. They've heard about the social credit score. They're all familiar with the lesson: "Don't write anything that you would not want to see on the front page of the newspaper."
I'm lucky that anything I ever wrote in school is now in the bit bucket.