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:
 
1.) http://www.education.com/reference/article/reading-magazines-children/
 
2.) http://www.education.com/magazine/article/11_Magazines_for_the_Elementary/
 
3.) http://www.parents-choice.org/award.cfm?thePage=magazine&p_code=p_per
 
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:
 
Get the Scoop! Create a Family Newspaper
http://www.education.com/magazine/article/Family_Newspaper/
 
I hope these resources are helpful to you and your 5th grader.

National Geographic for Kids
Sports Illustated for Kids
Ranger Rick
Time for Kids

Check out Nickelodeon magazine as well.

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.

highlights magazine is a good magazin for kids