If the design Code (ASME) has been specified by your client or user and if it is acceptable to the regulating bodies in your state/country, you can use ASME as the design code.
Although the pressure of the above tank is below the ASME VIII Div.1 limits, you are still allowed to design the tank as per rules and requirements of the Code and even you can stamp the tank (U Stamp) if you want to. All you need to design is to follow all rules of the ASME code. Take the design pressure equal to 5Psig in the Code formula and that's it!
However, be cautious about the minimum thicknesses and selected thicknesses. The ASME Code only gives you the minimum thicknesses required under pressure at the design temprature. But you might need to use much larger thicknesses due to handling and construction issues.






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