I have read your question over and over looking for something that would want to make a person move.
Why have you not spoken to the parents? The girl could get kidnapped.
Maybe the grandparent really locks her out so she can't go in to the bathroom and then "pretends" that she's mad that the girl went outside without her knowing.
A five year old "stealing" toys from your garage? At that age, do they know the difference between playing with available toys and stealing? Does she take them home? Close your garage door. Adults might wander in and steal things much more valuable.
So parents, let me know what you think about these recommendations:
Gather your courage to speak to the parents with the attitude that they don't know about it and you don't want to see this little girl kidnapped, etc.
Do not call CPS before talking to the parent. If you do talk to the parents and the child is still out everyday without supervision, then perhaps call the CPS to see if that is something that they respond to.
I know it may be shocking now but that is the way we kids did things in the 50's. But we had neighbors who cared and the parents all knew each other, had each other's phone numbers, and invited the kids in for board games, etc. Our biggest problem was the neighborhood bully whose parents weren't involved like the rest.
Stop quering the child.
Don't show your children how to handle this in the worst possible way. (You would remove your children away from their neighborhood friends, school friends, etc. and spend thousands of dollars realtors and closing fees, go through the stress and work of moving all your belongings all over a 5 year old who acts like an unsupervised 5 year old. Try to fix it, don't run from it. These problems aren't that bad. You might experience worse in another neighborhood from kids, to neighbors, to barking dogs, to vandalism, etc.