  The Grassmannian Gr(2,5) is embedded in $\Bbb{P}^9$ via the Pl\"ucker
embedding. The intersection of two general PGL(10)-translates of Gr(2,5) is a
Calabi-Yau 3-fold X, and the intersection of the projective duals of the two
translates is another Calabi-Yau 3-fold Y, deformation equivalent to X.
Applying results of Kuznetsov and Jiang-Leung-Xie shows that X and Y are
derived equivalent, which by a result of Addington implies that their third
cohomology groups are isomorphic as polarised Hodge structures. We show that X
and Y provide counterexamples to a certain "birational" Torelli statement for
Calabi-Yau 3-folds, namely, they are deformation equivalent, derived
equivalent, and have isomorphic Hodge structures, but they are not birational.
