Cu5(VO4)2(OH)4 (turanite) is a layered compound, exhibiting a copper(II) oxide layer in the [0 1 1] plane composed of edge-sharing CuO6 octahedra. Each Cu-O layer is further separated by VO4 tetrahedra. Closer scrutiny found that the copper(II) oxide layer in the compound represents a totally new geometrically-frustrated lattice, a 1/6 depleted triangular lattice. More specifically, the spin network in the [0 1 1] plane is formed by the alternate ranking of triangular and honeycomb strips. Magnetic measurements show that the Cu5(VO4)2(OH)4 behaves as a spin-1/2 ferrimagnet with a Tc = ∼4.5 K. It exhibits an unusual 1/5 magnetization plateau arising from the competition between antiferromagnetic and ferromagnetic interactions caused by the strong frustration. The possible spin-arrangements are also suggested.