  We have investigated the accretion of phantom energy onto a 5-dimensional
extreme Einstein-Maxwell-Gauss-Bonnet (EMGB) black hole. It is shown that the
evolution of the EMGB black hole mass due to phantom energy accretion depends
only on the pressure and density of the phantom energy and not on the black
hole mass. Further we study the generalized second law of thermodynamics (GSL)
at the event horizon and obtain a lower bound on the pressure of the phantom
energy.
