# is co-NSPACE(n^2) a strict subset of DSPACE(n^5)?

Is $$co-NSPACE(n^2) \subsetneq DSPACE(n^5)?$$

From Savitch theorem $$co-NSPACE(n^2) \subset DSPACE(n^4) \implies co-NSPACE(n^2) \subset DSPACE(n^5)$$

and as $$PSPACE = NPSPACE$$ we can go further to $$DSPACE(n^2)\subset DSPACE(n^5)$$ (and this observation already doesn't make sense for me as it's obvious...) but I'm stuck with it and dont know which steps should I take here.

I feel like the answer to the question is "yes, it is", and I think Space hierarchy $$DSpace(o(s2)) \subsetneq DSpace(s2)$$ might be useful here, but I do not know how to apply it. Maybe this proof should be done by a TM simulation? Any suggestions?