Yes, ISO 4288 is most likely correct though know that your German speaking customer is most likely referring to DIN EN ISO 4288.
Rz is the mean roughness depth and is measuring the total height or vertical distance from the highest peak to the lowest point or valley within a minimum of five sampling lengths, then averaging the peak-valley depths. This is not the same as Ra. Also, a Rz 5 is a aggressive manufacturing process, which may require honing, lapping, grinding or similar to achieve. My notes are based on the specified area and access to facilitate the manufacturing process should be considered.
"min 23" specification is not shown within your attachments so I'm guessing this is an Ra specification? If so the requirement is simply that the roughness should not be less than Ra 32 - probably Gasket surface of equivalent.