No, you do not get 5-6 mpg better for topping off your tank. You might travel more miles on that tank before you have to fill up, but the OP's original suggestion sounds as if it must be incorrect.

As chasingdal referred to generally, when a car has more weight to haul around (including the weight of the fuel in your tank), it takes more energy to move the car a given distance. You may 'seem' to get better gas mileage at the beginning of a tank than at the end of it, for a variety of reasons (it may be partly related to the way the gauge measures your mpg- too long to explain here why that can sometimes be misleading).

However, strictly from a physics perspective, it's pretty simple. You can flick a wiffle ball across a table and give it a pretty quick speed with very little force, but it would take a strong shove to get a bowling ball moving that fast. Likewise, if you're driving a big, heavy truck (or a passenger car with a lot of luggage, or one hauling a boat) it takes more energy to get it moving than if you drive a lighter car (leave your golf clubs and toolboxes at home! Don't lug them around needlessly in your trunk out of forgetfulness- you're wasting gas!), and so your mpg is going to be worse. Basic physics.

 

I gotta agree that over filling can not possibly yield better mileage, unless you over fill once and under fill the next time. The over filled tank would appear to get better mileage but appearances would be deceiving. Tanks are not directly comparable unless the both the beginning and ending fills are to the same level.