The Fifth Order was a division of the Cardassian military.
The Fifth Order was known for their sophisticated military encryption codes which used a recursive encryption algorithm that was comparable to Elgol-red and Courier Code 5-9. Fifth Order Military Codes were among the military codes ruled out as belonging to the communique received at Deep Space 9 from the Gamma Quadrant. (DS9: "In Purgatory's Shadow")
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