Lie algebras satisfying identities of degree 5

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Let Φbe an associative ring with unity, containing 1/6.We prove that every prime Lie Φ-algebra satisfying the identity [(yx)(zx)]x = 0is embedded as a subring of a special form in a three-dimensional simple Lie algebra over some field A. It follows that there exists no central simple Lie algebra which is not three-dimensional and the cube of every inner derivation in which is a derivation. It is proved that if a semiprime Lie algebra over a field Φsatisfies an arbitrary identity of degree 5 (not following from the anticommutativity and Jacobi identities), then it also satisfies the standard identity of degree 5. Essentially used in the proof is the notion of antiderivation. In passing we show that every prime Lie algebra having a nonzero antiderivation satisfies the standard identity of degree 5.