The diffeomorphism classification of smooth manifolds homeomorphic to CP^m is determined for m=5-8, and tangential homotopy types for m=4-8, with one non-homeomorphic for m=4 and two for m=8.
Brumfiel, DifferentiableS 1-actions on homotopy spheres, mimeographed notes, University of Cali- fornia, Berkeley, 1968
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Diffeomorphism Classification of Smooth Structures and Tangential Homotopy Types of $\mathbb{C}P^m$ for $5 \le m \le 8$
The diffeomorphism classification of smooth manifolds homeomorphic to CP^m is determined for m=5-8, and tangential homotopy types for m=4-8, with one non-homeomorphic for m=4 and two for m=8.