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The Somos 5 sequences are a family of sequences defined by a fifth orderbilinear recurrence relation with constant coefficients. For particular choicesof coefficients and initial data, integer sequences arise. By making theconnection with a second order nonlinear mapping with a first integral, weprove that the two subsequences of odd/even index terms each satisfy a Somos 4(fourth order) recurrence. This leads directly to the explicit solution of theinitial value problem for the Somos 5 sequences in terms of the Weierstrasssigma function for an associated elliptic curve.

Sigma function solution of the initial value problem for Somos 5 sequences