I was thrown by the topic of your post. For what it's worth: FRINDLE and WEDNESDAY WARS are what I'd call "perfect" middle grade -- and MOST middle have characters between 5th and 7th grade. (After all, 8/9-to-12 is the perfect middle grade target demographic!)
"Lower" middle grade means something else: That kind of book that is longer-than-a-chapter-book but might feel too young for a 12 year old. As in, DOLL PEOPLE by Ann M Martin, or THE WORLD ACCORDING TO HUMPHREY.
If you just want recommendations for middle grade starring fifth graders, you might want to change the name of your post for best results! :-)