Li-7 (and some Li-6) NMR studies have been performed at 16 MHz and 117 MHz and over an extended range of temperatures to explain the lithium dynamics in the novel crystalline thioborate Li5B7S13. Three different processes of motion have been found and characterized by analyzing both the NMR spectra and the (T-1(-1), T-1p(-1), T-2(-1)) relaxation rates. Suggestions for the assignment and comparisons with other crystalline and glassy lithium thioborates are given.