  Employing five commuting sets of five-qubit observables, we propose specific
160-661 and 160-21 state proofs of the Bell-Kochen-Specker theorem that are
also proofs of Bell's theorem. A histogram of the 'Hilbert-Schmidt' distances
between the corresponding maximal bases shows in both cases a noise-like
behaviour. The five commuting sets are also ascribed a finite-geometrical
meaning in terms of the structure of symplectic polar space W(9,2).
