The cubic spinel oxides Li(1+x)Ti(2-x)O(4) (0 < or =x< or = 1/3) are promising anode materials for lithium-ion rechargeable batteries. The end member of the Li-Ti-O series, Li(4)Ti(5)O(12), can accommodate Li ions up to the composition Li(7)Ti(5)O(12). Whereas a number of studies focus on the electrochemical behaviour of Li insertion into and Li diffusion in the Li intercalated material, only few investigations about low-temperature Li dynamics in the non-intercalated host material Li(4)Ti(5)O(12) have been reported so far. In the present paper, Li diffusion in pure-phase microcrystalline Li(4)Ti(5)O(12) with an average particle size in the microm range was probed by (7)Li solid state NMR spectroscopy using spin-alignment echo (SAE) and spin-lattice relaxation (SLR) measurements. Between T = 295 K and 400 K extremely slow Li jump rates tau(-1) ranging from 1 s(-1) to about 2200 s(-1) were directly measured by recording the decay of spin-alignment echoes as a function of mixing time and constant evolution time. The results point out the slow Li diffusion in non-intercalated Li(4)Ti(5)O(12) x tau(-1) (1/T) follows Arrhenius behaviour with an activation energy E(ASAE) of about 0.86 eV. Interestingly, E(ASAE) is comparable to activation energies deduced from conductivity measurements (0.94(1) eV) and from SLR measurements in the rotating frame (0.74(2) eV) rather than from those performed in the laboratory frame, E(A)(low-T) = 0.26(1) eV at low T.