This work settles the Eichler-Shimura congruence relation of Blasius and Rogawski for certain 5-dimensional Hodgetype Shimura varieties, that were not tractable by previously known methods. In a more general context we introduce a hypothesis called (N V C) on the behavior of Hecke correspondences, and show that it implies the congruence relation. A major ingredient in the proof of this result is a theorem of R.Noot on CM -lifts of ordinary points in characteristic p, along with an analysis of the (mod p)reductions of various Hecke translates of that CM -lift. Finally we prove this (N V C)-hypothesis for our particular Shimura 5-folds, and in doing so we obtain an unconditional result for the congruence relation of these non-P EL examples.