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We prove that if a smooth variety with non-positive canonical class can beembedded into a weighted projective space of dimension $n$ as a well formedcomplete intersection and it is not an intersection with a linear cone therein,then the weights of the weighted projective space do not exceed $n+1$. Based onthis bound we classify all smooth Fano complete intersections of dimensions $4$and $5$, and compute their invariants.

Bounds for smooth Fano weighted complete intersections