Elastocaloric cooling holds considerable promise as a compact, quick alternative to standard cryogenic refrigeration, though its practical implementation still requires considerable research on candidate materials and appropriate techniques for applying large, rapid strains at low temperatures. In this study a load-unload approach is used to induce substantial strains in a candidate cryogenic elastocaloric working material, TmVO${}_{4}$, at low temperatures. Employing this technique, the authors observe a giant elastocaloric response, cooling the material by 2.3 K at a bath temperature of 5 K. These results provide a starting point for practical elastocaloric cooling in the subkelvin regime.