A search for long-lived, massive particles predicted by many theories beyond the Standard Model is presented. The search targets final states with large missing transverse momentum and at least one highmass displaced vertex with five or more tracks, and uses 32.8 fb(-1) of root s = 13 TeV pp collision data collected by the ATLAS detector at the LHC. The observed yield is consistent with the expected background. The results are used to extract 95% C.L. exclusion limits on the production of long-lived gluinos with masses up to 2.37 TeV and lifetimes of O(10(-2)) - O(10) ns in a simplified model inspired by split supersymmetry.