The viscosity of the nematic liquid crystal PCH-5 [4-(trans-4'-pentylcyclohexyl)-benzonitrile], measured in the presence of an electric field parallel to the gradient of the velocity, shows a complex dependence both on magnitude E of the electric field and on the shear rate (gamma) over dot. When plotted versus E-2/(gamma) over dot, all data points fall unto a master curve. In nonequilibrium molecular dynamics computer simulations, performed for a Gay-Berne model fluid, the corresponding influence of a magnetic field on the viscosity was calculated. In both cases, the shape of the master curve for the viscosity can be computed by considering the competition between the torques exerted by the velocity gradient and by the orienting field. It involves the Leslie viscosity coefficients gamma(1) and gamma(2), the Miesowicz and Helfrich viscosities eta(1),eta(2), and eta(12). Thus it should be possible to extract these coefficients from the data. This is straightforward in the magnetic case since the molecules in the fluid "see" the externally applied field. The internal electric field, however, differs from the applied field E. When this effect is taken into account, using the known experimental values for dielectric coefficients epsilon(parallel to) and epsilon(perpendicular to), the electro-rheological master curve agrees very well with the experimental data. Values for the viscosity coefficients are obtained and presented.