  The vacuum Einstein equations in 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
$\mathbb{R}^{3+1} \times S^2$. 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 dimensions, due to a diverging Kretschmann scalar in
the initial data.
