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We construct an exactly solvable commuting projector model for a 4+1 dimensional Z2 symmetry-protected topological phase (SPT) which is outside the cohomology classification of SPTs. We show how to extract the topological invariant that characterizes the phase from the effective symmetry action on the boundary. Our method is quantum-information theoretic, with the invariant being an invariant of a quantum circuit that represents this effective boundary symmetry action. This gives a method for understanding such exotic SPT phases that is complementary to the usual field theory approach, which requires putting the system on non-trivial spacetime manifolds, which is difficult to formalize for lattice Hamiltonian models. We also discuss surface states which saturate the corresponding `t Hooft anomaly. I will try to make this talk pedagogical and accessible to an audience