Thank you for asking this question. I really enjoyed reading magazines as a child (my favorites were Ranger Rick and Highlights), and I still enjoy reading magazines to this day, including those I read with my daughter.
To answer your question, here are three listings of magazines for children, with age range and descriptions for each magazine:
I don't yet know of a newspaper specifically for 5th graders, but you might check with your child's teacher or your local librarian to see if he/she has any recommendations. Or, consider having your family create its own newspaper. Here is some info to get you started on that project:
For a world view, go to www.newsademic.com...a e-newspaper for young readers. I think it is simply fantastic, and you can sign up for a once every 2 weeks free cover story to be sent to you /your child and/or pay for a subscription which gives you fascinating articles about events - all delivered in a succint bottom line clear language for the 11 to 16 year olds.