  The Somos 5 sequences are a family of sequences defined by a fifth order
bilinear recurrence relation with constant coefficients. For particular choices
of coefficients and initial data, integer sequences arise. By making the
connection with a second order nonlinear mapping with a first integral, we
prove 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 the
initial value problem for the Somos 5 sequences in terms of the Weierstrass
sigma function for an associated elliptic curve.
