Admin approval of Commerce order
You might consider one of two methods:


Define another status/branch in the checkout logic (approved shopping cart -> checkout) wherein Rule 5 would redirect to the approved cart step instead of the standard shopping cart. 


or 


Implement an "admin approved" flag on the Order that you could set in your actions for Rule 5 and then test in your conditions for Rule 3, redirecting the user only if that flag was false. That flag could be implemented as a new field on the Order entity (assuming Order is an entity).  


Method 1 might be somewhat redundant and more work than method 2, but I think it's the better of the two because it extends the current shopping cart/checkout/Rules logic and workflow. I think there's merit in that. 

In addition, method 2 would bury a critical aspect of that logic into a field on the Order. I think the state of an Order in a checkout process should be defined separately from the Order itself.

Perhaps there's a third way that uses a little bit of both methods.

Hope this is helpful.