Well, these cases are generally known as English cases as they were produced either in Birmingham ( Dennison) or London (Shackman)
You will notice the difference in the medallion stars size and shape to your other watches - which is a dead give-away for an English or French case.
If you haven't seen it you may also like to read this essay by Desmond on Dennison cases
http://omega-constellation-collecto...01/from-advent-of-bretton-woods-monetary.html
it features your '.5004' reference, amongst others
However, if your's was produced late or later than '67 (the movt serial suggests ~'67) it could be a Shackman case as Dennison went bump in '67 and Shackmann took over their production.
The marks inside the case back will tell you which
A.L.D for Dennison
Stylised 'S' for Shackman
-and the hallmark date letter will give you the case production date (which could differ by some years to the movement serial date)