NO.... at this age, no teen shows are appropriate.
That is me. That is also the opinion of my daughter's Teacher's, whom I have asked.
MANY of the girls/boys in my daughter's classes, since Preschool (she is now 7 and in 2nd grade), watch these shows. It is obvious... in their dress and behavior and what they talk about.
At this age, they do not understand fully, the teen scenarios that are shown on tv.
Use common sense. Teen shows are for teens. Not younger.
I monitor what my kids watch. My daughter and I have viewed iCarly/Hannah Montana/Zack & Cody and those other shows. Her classmates, watch those. Even when they were only 4-5 years old. And I could tell, as well as my daughter's Teachers, WHICH kids watched those shows.
After my daughter & I watched those shows together, I talked with her about it and told her, she cannot watch it. It is for teenagers. Not her. She even agreed and understood.
My son who is only 3.5 years old... knows as well to not watch anything with teenagers and that it is not good for his age. He even tells us if an inappropriate commercial comes on.
We saw a Doctor once for my daughter, and he asked what kinds of posters she had on the wall and what shows she watches. He said, these 'teen' shows affects young children... and that it can affect their sexual development as well and ability to discern or not, what is appropriate or not, for their age. And quite simply, teen scenarios on TV are not in line with the mind of a 5-6 year old. It is beyond them.
Then sure, teen shows are for teens. But that does not mean it is good for them... so, you need to jointly talk about it and whatever you see on the TV, with them. Even watching the news... can be discussed with a child. So that they learn.... what is acceptable or not..... etc.
My kids, watch Noggin, the Upside Down show, Oobie, Max & Ruby, Little Bear, Gullah Gullah Island, Dora, Diego, Umizoomi, things like that.
The other kids in my daughter's class.... some say these shows "are for babies...." My daughter, is self-assured enough to know that she still likes these shows... and doesn't care what they say. She says they are 'sassy' kids who say that... and too precocious. Her Teacher, commented on it too. Saying the kids watch 'teen' shows and she can tell because of how they talk and what they talk about in class.
just some thoughts,
All the best,
Susan