Z is indeed a date code. 1957. A is 1934, B is 1935, etc. I and O are skipped due to their resemblance to digits 1 and 0.
5 is the district, D means a directional or distance sign, and then the serial number comes after that.
1957 is the first year that signs were made without the Division of Highways logo - the logo was taken off around March, 1957. The crossbar that separates destinations in different directions was added in 1955 or 1956. In 1958, the white porcelain signs were changed to green ones with white retroreflective legend.
in the general area of this white guide sign was the last known California/US porcelain cutout shield, as late as 2001!