In　this　paper,　we　study　a　quintic　Lienard　system　(x)over　dot　=　y,　(y)over　dot　=　-(a(0)x　+　a(1)x(3)　+　a(2)x(5))　(b(0)　+　b(1)x(2))y　with　Z(2)-equivariance,　arising　from　the　complex　Ginzburg-Landau　equation.　Although　this　system　is　a　versal　unfolding　of　the　germ　(x)over　dot　=　y,　(y)over　dot　=　-a(2)x(5)　+　O(x(6))　-　(b(1)x(2)　+　O(x(3)))y　near　the　origin,　it　cannot　be　changed　equivalently　into　a　near-Hamiltonian　system　for　global　variables　and　parameters　so　that　its　dynamics　cannot　be　studied　via　counting　the　isolate　zeros　of　Abelian　integrals　as　usual.　We　present　a　complete　study　of　this　system　with　a(2)　＜　0,　i.e.,　the　sum　of　indices　of　equilibria　is　-1,　and　show　that　this　system　exhibits　at　most　three　limit　cycles　and　a　double　center.　The　necessary　and　sufficient　conditions　are　obtained　on　the　existence　of　three　limit　cycles,　a　stable　two-saddle　heteroclinic　loop,　an　unstable　figure-eight　loop,　and　two　stable　homoclinic　loops.　A　global　bifurcation　diagram　and　the　corresponding　global　phase　portraits　in　the　Poincare　disc　of　this　system　are　given,　including　pitchfork　bifurcation,　Hopf　bifurcation,　transcritical　bifurcation,　twosaddle　heteroclinic　loop　bifurcation,　double　limit　cycle　bifurcation,　homoclinic　bifurcation,　saddle　connection　bifurcation,　and　degenerate　Bogdanov-Takens　bifurcation.　Note　that　the　dynamics　of　this　quintic　Lienard　system　is　so　complicated　that　it　has　infinitely　many　bifurcation　surfaces　of　saddle　connection.