  In this article we study genus 5 curves with a fixed point free involution.
We give two geometrical caracterisations of these curves amoung all genus 5
curves. One of these was conjectured by Arbarello, Cornalba, Griffiths and
Harris in their book on curves. The second one is given by some particular
embeddings corresponding to the points of the Prym variety associated to the
situation.
