The vacuum Einstein equations in $$5+1$$ 5 + 1 dimensions are shown to admit solutions describing naked singularity formation in gravitational collapse from nonsingular asymptotically locally flat initial data that contain no trapped surface. We present a class of specific examples with topology $$\mathbb {R}^{3+1} \times S^2$$ R 3 + 1 × S 2 . Thanks to the Kaluza–Klein dimensional reduction, these examples are constructed by lifting continuously self-similar solutions of the 4-dimensional Einstein-scalar field system with a negative exponential potential. The latter solutions are obtained by solving a 3-dimensional autonomous system of first-order ordinary differential equations with a combined analytic and numerical approach. Their existence provides a new test-bed for weak cosmic censorship in higher-dimensional gravity. In addition, we point out that a similar attempt of lifting Christodoulou’s naked singularity solutions of massless scalar fields fails to capture formation of naked singularities in $$4+1$$ 4 + 1 dimensions, due to a diverging Kretschmann scalar in the initial data.