Nuclear magnetic resonance and electrical conductivity measurements are conducted to study the dynamics of the ionic diffusion process in the crystalline ionic conductor Li_(0.05)La_(0.5)TiO_(3). dc conductivity shows a nonArrhenius temperature dependence, similar to the one recently reported for some ionic conducting glasses. Spin-lattice and conductivity relaxations are analyzed in the same frequency and temperature range in terms of the non-Arrhenius dependence of the correlation time. Both relaxations are then described using a single correlation function of the form f(t)=exp(-(t/τ)^(β)), with β=0.4 over the whole temperature range.