Is there a hydraulic advantage with using a pressurized fuel tank (diagram included)?

I want to build a box shaped fuel tank that can hold 20 gallons of fuel and supply fuel to a car without the need for mechanical fuel pumps. It has a fuel outlet fitting at the bottom (1/4" diameter), and an air inlet fitting at the top (1/4" diameter). If I fill it up with fuel, and then pressurize this vessel with 5 psig (lb/in^2 gauge pressure) of air, what will the resultant pressure be at the outlet fitting? The air exerts force on the fuel's surface area of 100 square inches. Please see the picture I drew.

Thinking about this without using math it seems intuitive to me that a small amount of air pressure exerted over a large surface area would cause the pressure of the liquid fuel to be substantially higher than the air that is pressurizing it, but I have not found any proof of this, nor mathematical formula that can be used to calculate the resultant pressure.