A preparation of allogeneic T-lymphocytes that have been transduced with a lentiviral vector to express a chimeric antigen receptor (CAR) consisting of a humanized anti-CD5 single chain variable fragment (scFv) domain linked to a interleukin (IL)-15/IL-15sushi domain and a safety switch, with potential immunostimulating and antineoplastic activities. Upon administration, the allogeneic anti-CD5-IL-15/IL-15sushi-safety switch CAR T cells target and bind to CD5-expressing tumor cells, thereby inducing selective cytotoxicity in CD5-expressing tumor cells. The IL-15/IL-15sushi domain activates and increases the levels of natural killer (NK) cells and memory CD8+ T-cells. The memory T-cells enhance the secretion of the cytokine interferon-gamma (IFN-g), which further potentiates the immune response against tumor cells. This may increase tumor cell killing and decrease tumor cell proliferation. The pro-survival cytokine IL-15 regulates CD8+ T and NK cell development, activation and proliferation. The safety switch, composed of two rituximab (RTX)-binding epitope sites, allows for the selective elimination of the CAR-T cells through the administration of RTX. CD5, a T-cell associated antigen, is expressed in many T-cell lymphomas and leukemias.