This is a multi-center, open-label, non-randomized, phase 1/2 study of anti-CD5 CAR-T cell therapy in patients with CD5+ relapsed or refractory T-cell malignancies. A bayesian optimal interval (BOIN) 12 design will be used to explore the optimal biological dose (OBD) from starting dose level 1: 1×10^6 (±20%) to dose level 2: 2×10^6 (±20%) in three cohorts (autologous, previous-transplant-donor or newly matched donor-derived CD5 CAR T cells). If the manufactured cells are not sufficient to meet the preassigned standard dose criteria, patients will be given infusion at a low dose level of 5×10^5 (±20%) /kg. The primary objective is to evaluate the safety and tolerability of CD5 CAR T cell therapy in subjects, determine the OBD and recommend phase 2 dose (RP2D) in phase 1, and evaluate the efficacy of CD5 CAR T cell therapy in phase 2. The primary endpoint is the type and incidence of dose-limiting toxicity (DLT) within 28 days, and the incidence and severity of adverse events (AEs) within 30 days after CD5 CAR T-cell infusion in phase 1, the best overall response (BOR) at 3 months (± 1 week) after CD5 CAR T-cell infusion in phase 2. A total number of 54 subjects will be enrolled.

Inclusion Criteria:

Only patients who meet all the following criteria can be included:

1. Candidates with relapse or refractory CD5+ T-cell malignancies, who have progressed after treatment with all standard therapies or been intolerant of standard care, have limited prognosis with currently available therapies and have no available curative treatment options (such as stem-cell transplantation (SCT) or chemotherapy);
2. For subjects who received autologous CD5 CAR T cells, the tumor burden in peripheral blood is less than 20%, and suspending anti-neoplastic treatment for more than 2 weeks;
3. Aged 1-70 years;
4. No severe allergy;
5. Eastern Cooperative Oncology Group (ECOG) performance status 1 score 0 to 2;
6. Patients are expected to live for at least 60 days;
7. CD5+ on blasts in bone marrow (BM) or cerebrospinal fluid (CSF) and tumor tissues by flow cytometry and immunohistochemistry, respectively. (Positive rate >80% by flow cytometry with less than one log difference in mean fluorescence intensity from normal T cells, or positive rate >30% positive by immunohistochemistry);
8. Provide a signed informed consent before any screening procedure. Subjects who voluntarily participate in the study should have the ability to understand and sign the informed consent form and be willing to follow the study visit schedule and relevant study procedure, as specified in the protocol. Candidates aged 19-70 years need to be sufficiently conscious and able to sign the treatment consent form and voluntary consent form. Children candidates of 8-18 years old need to be sufficiently conscious and able to sign the treatment consent form and voluntary consent form and their legal guardian or patient advocate has also need to sign the treatment consent form and voluntary consent form, respectively. Children candidates of 1-7 can be recruited after the legal guardian or patient advocate has signed the treatment consent form and voluntary consent form;
9. Have available allogeneic hematopoietic stem cell transplantation donor for the subject who received newly matched donor-derived CD5 CAR T cells, and is willing to perform SCT when CR is achieved.

Exclusion Criteria:

Patients with at least one of the following conditions are excluded:

1. Impaired consciousness or intracranial hypertension;
2. Symptomatic congestive heart failure or severe cardiac arrhythmia;
3. Manifestations of severe respiratory system failure;
4. Co-existence with other malignancies;
5. Disseminated intravascular coagulation;
6. Serum creatinine and/or blood urea nitrogen (BUN) ≥ 1.5-fold upper limit;
7. Sepsis or other uncontrollable infections;
8. Uncontrollable diabetes;
9. Serious mental illness;
10. Apparent and active intracranial lesions on cranial magnetic resonance imaging (MRI);
11. Underwent organ transplantation, excepting SCT;
12. Pregnant females;
13. Positive test for infectious hepatitis, acquired immune deficiency syndrome (AIDS) or syphilis;
14. Post-CAR SCT is not feasible in patients who plan to receive newly matched donor-derived CD5 CAR T cells;
15. Inability to collect peripheral blood mononuclear cells (PBMC) or no frozen PBMC available for CAR T cell manufacturing.