The 5 mol % MgO:LiNbO3 ferroelectric single crystal has attracted much attention in terahertz (THz) generation and detection by parametric process or optical rectification. In this work, the dielectric properties of 5 mol % MgO:LiNbO3 ferroelectric single crystal in 0.2-2 THz frequency range has been investigated by using transmission-type THz time-domain spectroscopy. The complex refractive index and dielectric function are extracted from the measured transmittance and phase shift. The power absorption and dispersion relationship of the lowest branch of the phonon polariton are observed. The results fit well with the classical damped oscillator model, indicating that the far-infrared dielectric response of 5 mol % MgO:LiNbO3 is dominated by the lowest transverse optical mode with E(x,y) symmetry centered at 4.533 THz. The investigation presented in this work provides important considerations for optimizing THz devices in 5 mol % MgO:LiNbO3 ferroelectric single crystal.