  As we know that the Lovelock theory is an extension of the general relativity
to the higher-dimensions, in this theory the first and the second order terms
correspond to the general relativity and the Einstein-Gauss-Bonnet gravity,
respectively. We obtain a $5D$ black hole solution in Einstein-Gauss-Bonnet
gravity surrounded by the quintessence matter, and also analyze their
thermodynamical properties. Owing to the quintessence corrected black hole, the
thermodynamic quantities have also been corrected except for the black hole
entropy, and phase transition is achievable. The phase transition for the
thermodynamic stability, is characterized by a discontinuity in the specific
heat at $r=r_C$, with the stable (unstable) branch for $r < (>) r_C$.
