Here is the memory that is recommended by Crucial Memory:
http://www.crucial.com/usa/en/compatible-upgrade-for/HP-Compaq/hp-prodesk-405-g1-tower
http://www.crucial.com/usa/en/compatible-upgrade-for/HP-Compaq/hp-prodesk-405-g2-mt
Since I wasn't certain which is your version of the ProDesk 405, I gave you a link to both versions. Make certain to choose the correct one.
Crucial makes very good, reliable memory. Since the memory is so inexpensive, I suggest buying all new memory so there is no conflict with the old and new memory.
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