Simple Lie algebras satisfying the standard Lie identity of degree 5

A description is given of simple Lie algebras over fields of characteristic different from two that satisfy the identity
$$ \sum_{\sigma\in S_4}\operatorname{sgn}(\sigma)[z,x_{\sigma(1)},x_{\sigma(2)},x_{\sigma(3)},x_{\sigma(4)}]=0. $$

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