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 high-mass displaced vertex with five or more tracks, and uses 32.8 fb$^{-1}$ of $\sqrt{s}$ = 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\% CL exclusion limits on the production of long-lived gluinos with masses up to 2.37 TeV and lifetimes of $\mathcal{O}(10^{-2})$-$\mathcal{O}(10)$ ns in a simplified model inspired by Split Supersymmetry.
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