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We determine the most general solution of the five-dimensional vacuumEinstein equation, allowing for a cosmological constant, with (i) a Weyl tensorthat is type II or more special in the classification of Coley et al., (ii) anon-degenerate "optical matrix" encoding the expansion, rotation and shear ofthe aligned null direction. The solution is specified by three parameters. Itis locally isometric to the 5d Kerr-de Sitter solution, or related to thissolution by analytic continuation or taking a limit. This is in contrast withfour dimensions, where there exist infinitely many solutions with properties(i) and (ii).

Uniqueness of the Kerr-de Sitter spacetime as an algebraically special solution in five dimensions