The nucleosynthesis occurring in type-I X-ray bursts (XRBs) and the respective energy released in these thermonuclear explosions are sensitive to nuclear masses and reaction rates around the $^{64}$Ge waiting point. Based on the recently measured masses of $^{64}$Ge and $^{65}$As, the deduced proton separation energies $S_p$($^{65}$As) and $S_p$($^{66}$Se), and nuclear structure information from large-scale shell model calculations, we have obtained new reaction rates of $^{64}$Ge$(p,\gamma)$$^{65}$As and $^{65}$As$(p,\gamma)$$^{66}$Se with reliable uncertainties. Our new thermonuclear reaction rate of $^{64}$Ge$(p,\gamma)$$^{65}$As differs from those available in REACLIB by up to two orders of magnitude at temperature range associated with type-I X-ray bursts. We evaluated the impact of these new rates, particularly the energy generation and the burst light curve, with self-consistent one-zone model [Schatz et al. Phys. Rev. Lett. 86 (2001) 3471]. Also, we identified the nuclear physics uncertainties determining the role of the $^{64}$Ge to be a waiting point in XRBs, and strongly affecting XRB model predictions of the synthesis of $^{64}$Zn and the synthesis of nuclei $A\geq64$.