The invention provides methods of depleting CD5+ cells in human patients undergoing chimeric antigen receptor (CAR) immunotherapy in order to promote acceptance of CAR expressing immune cells. Anti-CD5 antibody drug conjugates (ADCs) are administered as a conditioning regimen to a human patient receiving autologous or allogeneic CAR expressing immune cells such that the CAR expressing immune cells are accepted by the human patient. Compositions and methods of the invention can be used in combination with CAR therapy to treat a variety of pathologies, including autoimmune diseases and cancer.