The problem is that the $5000 isn't being distributed evenly. The schools that rich kids go to, public or private, get orders-of-magnitude more funding than the ones poor kids go to.
Do you have figures? I very much doubt if that is the case.
Just checked for Pennsylvania (2009-10 academic year), and while the biggest spenders are over double the lowest spenders, there are no order-of-magnitude-difference pairs. Also, only two of the top ten spenders (per student) were in the top 10% academically.