The fresnel rings or rough side should face the gg.
But I dont think the Technika came from the Linhof factory with a fresnel. I may be wrong, but Im guessing your fresnel was added later. In that case, the fresnel could be placed either in front of (on the lens side) or behind the ground glass.
If it is behind the ground glass, which is most likely because it would not change the focal plane, the order, starting from the lens side, is: ground glass rough or matte side, ground glass shiny side, fresnel ringed or rough side.
If it is in front of the gg, which is the more traditional method, the gg would have to account for the thickness of the fresnel for proper focal plane positioning. The order, starting from the lens side, should be: fresnel shiny side, fresnel ringed or rough side, gg rough or matte side, gg shiny side.
Im not familiar with the version 5 of the Tech III, but on an earlier Technikas that I have seen, the gg was mounted under a hold-down bar mounted on the inside of the frame (toward the lens) which was screwed to the frame. The gg was mounted under this hold-down bar, with the spring under the gg pushing between the gg and the frame. I hope this makes sense. The order would be, starting from the lens side: hold-down bar, gg rough or matte side, gg shiny side, spring clip, frame back.
If the Technika came from the Linhof factory with a fresnel, then disregard the above. It must only be reinstalled as per the factory.
And finally, I hope you watched for small shims which may have been placed under the hold-down bar for proper spacing.