Dispersion causes optical pulses broadening and must be compensated for in long-distance high-speed optical data transmission systems. We investigate optical properties of micro structured fiber with 5-fold symmetric quasicrystal lattice of air-holes in a silica matrix for the first time. Dual-Concentric core Photonic Quasicrystal Fiber (DC-PQF) lattices with varying hole diameters were investigated and curves for the effective index, dispersion parameter and confinement losses were calculated by finite element method. For dispersion compensation purpose, we have proposed a novel 5-fold PQF with a high negative dispersion values ≈ 16,000 ps/(nm-km) could be reached for the wavelength around 1310 nm.