The liquid crystal 4-cyano-4′-pentylbiphenyl (5CB) is investigated regarding its nonlinear dielectric behavior as reflected in the dependence of the static dielectric constant ε_s on the magnitude of the electric field. The initial flow-induced homogeneous orientation of nematic domains can be erased by moderate electric fields, yielding states with little to no preferred orientation. Such samples are then subjected to ac and dc electric fields of various amplitudes, covering more than four orders of magnitude, between <10 V cm⁻¹ to 220 kV cm⁻¹. Their regime of linear dielectric response, i.e., field invariant static permittivity, is limited to fields <10 V cm⁻¹, equivalent to a voltage <50 mV_rms across a 50 μm thick sample. The Piekara factor, which gauges the sensitivity of ε_s to E², is a factor of 10⁸ times larger at low fields than its counterpart at elevated fields, where the nematic domains are highly aligned in homeotropic orientation. After removing the electric field, the nematic system returns to a state with little residual alignment, as judged by the dielectric constant settling near the value of the orientational average, 〈ε〉 = (ε_|| + 2ε_⊥)/3, and not far from that of the isotropic phase, ε_iso. The structural recovery associated with a field induced change in alignment is slow compared with dipole reorientation. For a different nematogen, itraconazole, no such extreme sensitivity to electric fields is found.