This is an investigator-initiated dose-finding clinical study with the primary objective of evaluating the safety of CD5CART in the treatment of subjects with relapsed and refractory CD5 hematological malignancies and to explore the MTD of CD5CART treatment of relapsed and refractory subjects with CD5 hematological malignancies. At the same time, the effectiveness and pharmacokinetic characteristics of CD5CART treatment of relapsed and refractory CD5 hematological tumors in subjects were explored

Inclusion Criteria:

Subjects must meet all of the following criteria to be enrolled:

1. CD5-positive B-cell lymphoma: B-cell lymphoma confirmed according to the National Comprehensive Cancer Network (NCCN) B-cell lymphoma clinical practice guidelines (2020 1st edition), and the tumor surface expresses CD5 (the test results within 60 days before signing the notice are acceptable for clinical practice, and the investigator will judge whether the test results of other hospitals are acceptable and whether they can be enrolled); According to the 2014 Lugano criteria, patients with B-cell lymphoma have at least one measurable lesion with a longest diameter ≥ 1.5 cm or bone marrow flow cytometry suggests bone marrow invasion, including:

1. Chronic lymphocytic leukemia/small lymphocytic lymphoma: Received any BTK inhibitor for at least 6 months and was ineffective (disease is in SD or PD state).
2. Mantle cell lymphoma: Relapsed/refractory disease with at least one treatment regimen, prior treatment must include chemotherapy with anthracyclines or bendamustine, anti-CD20 monoclonal antibody, and therapy with any BTK inhibitor.
3. Diffuse large B-cell lymphoma: Patients with diffuse large B-cell lymphoma who have refractory or relapsed after at least second-line therapy (one standard chemotherapy regimen and one salvage chemotherapy). At the same time, one of the following conditions is met: a. Unable to receive autologous hematopoietic stem cell transplantation; b. Refusal to receive autologous hematopoietic stem cell transplantation; c. Relapse after autologous hematopoietic stem cell transplantation.

2. CD5-positive T-cell lymphoma: Peripheral T-cell lymphoma confirmed according to the 2016 WHO classification criteria and the tumor surface expresses CD5 (if the current clinical practice is not suitable for sampling, the test results within 60 days before signing the information are acceptable, and the investigator will judge whether the test results of the other hospital are acceptable and whether they can be enrolled); According to the 2014 Lugano criteria, patients with T-cell lymphoma have at least one measurable lesion with a longest diameter ≥ 1.5 cm and no bone marrow invasion determined by bone marrow flow cytometry and receptor gene rearrangement (TCR/IGH) testing (and if PET-CT is available, it must not indicate elevated bone marrow metabolism); Refractory or relapsed after at least first-line therapy, including, but not limited to, the following peripheral T-cell lymphomas:

1. Peripheral T-cell lymphoma (non-specific type)
2. angioimmunoblastic lymphoma
3. ALK-negative mesentomas large cell lymphoma
4. extranodal NK/T-cell lymphoma
5. enteropathy-associated T-cell lymphoma
6. Large granular T lymphocytic leukemia
7. Other CD5 T-cell tumors such as adult T-cell leukemia, such as acute T-lymphoblastic leukemia/T-lymphoblastic lymphoma, etc 3. Age ≥ 18 and ≤ 70 years old, male or female. 4. Expected survival ≥ 12 weeks. 5. Serum total bilirubin ≤ 37.2 μmol/L (serum total bilirubin ≤ 3.0 ULN and direct bilirubin ≤1.5 ULN in patients with Gilbert syndrome), estimated glomerular filtration rate eGFR (CKD-EPI) ≥ 30 ml/min/1.73m2, alanine aminotransferase and aspartate aminotransferase are less than 2.5 times the upper limit of the normal range.

6. ECOG score 0-1 points. 7. Left ventricular ejection fraction (LVEF) ≥ 50% of the subjects diagnosed by echocardiography; Blood oxygen saturation > 91%.

8. Subjects and their spouses agree to take effective tools or drug contraceptives within one year after the subject signs the informed consent form until one year after CAR-T cell retransfusion; Female subjects of childbearing potential must have a negative serum or urine pregnancy test during the screening period.

9. Volunteer to participate in this trial and sign the informed consent form.

Exclusion Criteria:

Subjects who meet any of the following criteria will be excluded:

1. Those who have a history of allergy to any component of cell products.
2. Grade II-IV. acute GVHD determined by Glucksberg criteria or grade B-D severity determined by IBMTR index; Patients with acute or chronic GVHD who required systemic treatment within four weeks prior to enrollment.
3. Subjects who have been injected with live vaccines within 4 weeks before enrollment.
4. Central nervous system diseases that are not related to lymphoma central invasion (such as brain aneurysm, epilepsy, stroke, Alzheimer's, psychosis, etc.). Lymphoma central invasion or gastrointestinal invasion is not used as an exclusion criterion, but enrollment is at the discretion of the investigator.
5. Serious active infection (except uncomplicated urinary tract infection, bacterial pharyngitis), or currently receiving intravenous antibiotic therapy. However, prophylactic antibiotic, antiviral, and antifungal treatment for infections is allowed.
6. Hepatitis B surface antigen (HBsAg) positive or hepatitis B core antibody (HBcAb) positive and peripheral blood hepatitis B virus (HBV) DNA detection value > 100 IU/mL.
7. Those who are positive for hepatitis C virus (HCV) antibody and positive for hepatitis C virus (HCV) RNA in peripheral blood.
8. Subjects with other acquired and congenital immunodeficiency diseases, including but not limited to those who are positive for human immunodeficiency virus (HIV) antibodies; Subjects with cytomegalovirus (CMV) DNA detection value > 400 copies/mL; Those who test positive for syphilis.
9. Subjects with cardiac insufficiency of class III or IV according to the New York Heart Association (NYHA) cardiac function grading criteria (see Appendix 2).
10. Subject has a history of other primary cancers, except for the following:

1) Non-melanoma cured by resection such as basal cell carcinoma of the skin; 2) Cured carcinoma in situ such as cervical cancer, bladder cancer or breast cancer, etc.; 3) No recurrence of other primary cancers after treatment for more than 5 years.

11. History of solid organ transplantation. 12. Subjects with previous autoimmune diseases (mainly cellular immune abnormalities), immunodeficiency or subjects requiring immunosuppressant therapy.

13. Receiving other interventional clinical trial drugs within 3 months before signing the informed consent form (ICF); 14. Women who are pregnant or breastfeeding; 15. Suffering from mental illness or consciousness disorder or central nervous system disease; 16. Previous treatment toxicity has not been resolved to baseline or grade ≤2 (NCI-CTCAE v5.0, except alopecia); 17. Medication use:

1. Steroid medications: Therapeutic doses of steroids were used within 72 hours prior to CAR-T cell infusion, but physiologic doses of steroid supplementation are allowed (< 12mg/m2/day of hydrocortisone or its equivalent;
2. Systemic anti-tumor therapy requires at least 2 weeks or 5 half-lives of the drug before T cell collection (except for BTK inhibitors in CLL); T cells were collected from immune checkpoint inhibitors with an interval of less than 3 drug half-lives.

18. Active pulmonary infection. 19. Contraindications to peripheral blood apheresis. 20. Subjects who are considered unsuitable to participate in this trial by the investigator after careful consideration.