A scheme for realizing high-order nonlinear diffraction harmonics in a nonlinear photonic crystal is described. Based on the multiple conical fourth-order harmonics observed, the feasibility of realizing the fifth-order and sixth-order harmonics via nonlinear diffraction is theoretically analyzed. The simultaneous generation of red, green, and blue conical harmonics is observed under only one input laser beam, which is beneficial to the realization of three primary colors, continuous harmonics and even ring white light sources. The blue conical output harmonics may be attributed to the cascaded nonlinear diffraction process of fifth-order harmonic involving the reciprocal vectors. Under the same fundamental wavelength, the conical angle of the fifth-order nonlinear cerenkov harmonic is always larger than those of the other lower-order harmonics. Moreover, there always exists a minimum conical angle for the fifth-order nonlinear cerenkov harmonics under different input wavelengths. When the input fundamental wavelength is 3319.5 nm, the generation process for the fifth-order harmonic e light is corresponding to nonlinear Bragg diffraction, which is helpful for the effective generation of a sixth-order nonlinear diffraction harmonic.