The present invention is directed to the field of immunotherapy, in particular, adoptive T cell therapy or T cell receptor (TCR) gene therapy of cancer. The invention provides a nucleic acid encoding at least one TCR alpha or beta chain construct of a TCR construct capable of specifically binding to a peptide from the T-cell lineage specific antigen CD5, preferably SEQ ID NO: 1, in the context of a human MHC I such as HLA-A*02, in particular HLA-A*02:01. The invention also provides corresponding proteins and host cells, preferably, CD8+ T cells, expressing said TCR construct. Treatment optionally is in the context of allogeneic stem cell transplantation, in particular, mismatch-transplantation, or haploidentical transplantation, or in combination with an agent capable of inhibiting expression of HLA-A*02 in the TCR-transgenic T cells. The invention thus also provides compositions and kits comprising the nucleic acids of the invention in combination with an agent capable of inhibiting expression of HLA-A*02, and, as well as the medical use of such compositions and kits. The nucleic acids, compositions and kits, proteins or host cells may be for use in the diagnosis, prevention and/or treatment of a CD5-positive T-cell lymphoma or T-cell leukemia, no matter whether the antigen is expressed on the cell surface, intracytoplasmic or in both manners.