That's almost the exact age range between me and my beloved older sister.

When she was 11 and I was 5, we liked to:
Play with Barbies
Have someone read to us or tell us stories
Try to tell stories ourselves, but they were never quite as good as the ones a more sophisticated older friend or parent could tell
Cook stuff like cookies or cake mixes or frozen pizza with someone older helping and supervising
Do artsy-crafty stuff like stringing beads, drawing on the driveway with chalk, or painting things
Color in coloring books
Play kickball, softball, soccer, or basketball with other kids
Build card houses or set up dominoes or blocks all over the house and then knock them down
Set up TV trays or picnic benches in the yard and run hurdles
Play the piano and do simple duets
Play school with my older sister always the teacher. This really worked better with other kids because I tended to be a problem student
Climb trees
Jump rope
Make beds for our cats by putting pillows and towels in cardboard boxes and then try to get the cats to sleep or at least sit still in them
Ride bikes
Watch Disney movies
Play with makeup and/or nail polish
Play simple board gmes
Make mixtures (this we usually had to do on the sly and we often got busted). But we liked to get bowls and then start mixing lotion, powder, red food coloring, glitter, marbles. Anything we could find.
Play dress-up
Pretend to hypnotize each other and/or hold seances
Play hide and seek
Have water-gun battles
Have silly string battles (in the driveway only)
Make tape recordings or stage live performances of singing, lip-synching, or theatrical performances. Anything to hear outselves making noise. My dad had a microphone that we loved to use.

That's are just a few of some of the fun times I remember with my sister at those exact ages. We had a lot of fun!

I can't wait to hear about your "adventures," BFA. You're so creative and great, I'm sure they're going to have a ball!