A phase 2, open-label, multicenter study of MB-105 in patients with CD5 positive (CD5+) relapsed / refractory T-cell lymphoma (r/r TCL).

Inclusion Criteria: 1. Male or female ≥ 18 years of age. 2. Patients with r/r TCL per WHO 2022 criteria. 1. r/r CTCL that has failed ≥ 2 prior lines of standard of care (SoC) therapy. 2. r/r PTCL that has failed ≥ 1 prior lines of SoC therapy. Note: patients with CD30+ disease should have received brentuximab vedotin. 3. Has available tumor tissue or willing to undergo biopsy procedure. 4. CD5 positivity confirmed by local laboratory using an approved diagnostic test or LDT. 5. Karnofsky performance score ≥ 70% or higher. 6. Prior CAR T-cell therapy must have occurred \> 60 days prior to study enrollment and must have no evidence of CAR persistence. 7. Measurable or detectable disease 1. PTCL per Lugano criteria 2. CTCL per Global (ISCL/EORTC/USCCL) criteria. 8. Prior autologous or allogenic hematopoietic stem cell transplant (HSCT) must have occurred more than 60 days prior to study enrollment. 9. Adequate bone marrow function defined as: 1. Absolute neutrophil count (ANC) ≥ 1500/μL (≥ 1000/μL for patients with prior HSCT or marrow involvement) 2. Absolute lymphocyte count ≥200 cells/μL 3. Hemoglobin ≥ 8 g/dL (transfusion permitted) 4. Platelet count ≥ 75 000/μL (≥50 000/μL for patients with marrow involvement). 10. Organ function as follows: 1. Cardiac: left ventricular ejection fraction (LVEF) ≥ 50% by Echo or radionuclide scan. 2. Pulmonary: oxygen saturation ≥ 92% (room air). 3. Renal: calculated creatinine clearance \> 30 mL/min. 4. Liver:
*  Total bilirubin \< 1.5 x ULN (\< 2 × upper limit of normal (ULN)) if liver involvement).
*  If no liver involvement and total bilirubin ≥1.5 x ≤ ULN, direct bilirubin \< ULN (Gilbert syndrome)
*  Aspartate aminotransferase / alanine aminotransferase \< 3 × ULN (5 x ULN if liver involvement).
*  Albumin \> 2.5 g/dL. 11. For females of childbearing potential (defined as \< 24 months of amenorrhea or not surgically sterile \[absence of ovaries and/or uterus\]), a negative serum pregnancy test must be documented at screening, and prior to lymphodepletion (conditioning). 12. For females of childbearing potential and males, a highly effective method of contraception together with a barrier method must be used from the start of lymphodepletion (conditioning) and for at least 12 months after the last dose of study agent.

Exclusion Criteria: 1. Sezary syndrome. For other tumor types, if there is a suspicion of significant circulating disease at time of leukapheresis, discuss eligibility with medical monitor prior to proceeding. 2. Contraindication to leukapheresis. 3. Prior treatment with any CD5-targeted therapy. 4. Any evidence of the following active viral infections: 1. HIV infection. 2. Chronic hepatitis B virus (cHBV) infection with detectable viral load. Patients with cHBV, who are receiving anti-viral prophylaxis, may be enrolled if they are asymptomatic for \>5 days prior to signing informed consent (ICF). 3. Hepatitis C (HCV) infection with detectable viral load. Patients cured of HCV may be enrolled. 5. Presence of any active, uncontrolled systemic bacterial, viral or fungal infection requiring intravenous (IV) anti-infectives, including clinically significant viral infection or uncontrolled viral reactivation of Epstein-Barr virus, Cytomegalovirus, Adenovirus, BK-virus, or Human herpesvirus 6. If treated with anti-infective agents, patients must be asymptomatic for \>5 days prior to enrollment. 6. History of other cancer unless disease-free survival ≥ 2 years (cured non-melanoma skin cancer, in situ breast, non-muscle-invasive bladder or in situ cervical cancer are eligible to enter the trial without time limitations). 7. History of hypersensitivity reactions to products containing murine proteins. 8. Active CNS lymphoma. 9. Evidence of acute graft versus host disease (aGVHD) \> Grade 2 Mount Sinai Acute GVHD International Consortium (MAGIC) or chronic GVHD \> mild (NIH) requiring ongoing systemic steroids and/or multiagent therapy. 10. Patients who have received systemic immunosuppressive therapy for treatment of GVHD within 28 days of leukapheresis. 11. Currently requiring systemic corticosteroid therapy (10 mg/day or less of prednisone or equivalent doses of other systemic steroids are allowed for control of non-exclusionary pre-existing conditions). A 2-week washout is required prior to leukapheresis and prior to lymphodepletion for patients on \> 10 mg/day prednisone equivalent. 12. Patients who have received donor lymphocyte infusions within 28 days of MB-105 infusion. 13. Comorbidity that would impair the patient's ability to receive or tolerate MB-105 and/or affect participation in the study: 1. History of cardio- or cerebrovascular disease including myocardial infarction, unstable angina, or congestive heart failure (NYHA class III-IV) within 6 months or cerebrovascular accident (CVA; stroke) within 12 months prior to informed consent. 2. History of central nervous system (CNS) disorder(s) such as an uncontrolled seizure disorder, dementia, cerebellar disease, or any autoimmune disease with CNS involvement. 3. Any serious underlying medical or psychiatric condition deemed by the investigator and medical monitor to be exclusionary due to risk to the patient or to protocol compliance. 14. History of autoimmune disorders, including rheumatic diseases and thyroid disorders (though patients with a history of thyroid disease who have undergone successful therapy may be suitable). Exemptions for mild or limited disease may be granted after discussion between the Investigator and sponsor's medical monitor. 15. Participated in active treatment on other interventional research clinical trials \< 30 days before enrollment (participation in follow-up permitted).