I am installing a Liquid Nitrogen Freezer and it requires the pressure from tank to be 22 PSI.

My client purchased the tank from different supplier and relief valve on the tank is set at 5 bar.

Will this pressure from tank not damage my freezer as it requires only 22 PSI which is 5 bar?

 

Not an expert on this, but I suspect that the tank's pressure relief is there to protect the tank, not the process.

How is the tank pressurized? If by your own process, then you have control of the pressure in the tank and can set it to 22psi. If it's higher (and if it's a storage tank, I would probably expect that), you will need a pressure regulator between the tank and your process.