This is an open-label phase I study to determine the safety and recommended phase 2 dose (RP2D) of Senza5 CART5 cells in patients with relapsed or refractory CD5 positive nodal T cell NHL. RP2D will be based on the safety, tolerability, pharmacokinetics, and preliminary efficacy of Senza5 CART5 cells. This trial will evaluate up to 5 dose levels using the Bayesian Optimal Interval (BOIN) design enrolling 3 patients in each cohort to assess safety and achieve therapeutic levels so that the RP2D of Senza5 CART5 cells given as a single IV infusion can be determined.

Inclusion Criteria:

1. Histologically or cytologically confirmed relapsed or refractory (r/r) CD5-positive nodal peripheral T-cell lymphoma (such as peripheral T-cell lymphoma-not otherwise specified (PTCL-NOS), nodal T-cell lymphomas with T-follicular helper (TFH) phenotype, including follicular T cell lymphoma, angioimmunoblastic lymphoma, or anaplastic large cell lymphoma) or other non-leukemic CD5+ aggressive mature T cell lymphomas (such as enteropathy-associated T cell lymphoma, monomorphic epitheliotropic intestinal T cell lymphoma, transformed mycosis fungoides, primary cutaneous aggressive epidermotropic CD8+ cytotoxic T-cell lymphoma, primary cutaneous insert gamma delta symbols lymphoma, or subcutaneous panniculitis like T cell lymphoma).
2. ≥50% expression of CD5 on flow cytometry or IHC on malignant cells on the most recent biopsy
3. Must have received at least one line of prior systemic therapy for their lymphoma; participants with anaplastic large cell lymphoma (ALCL) must have received prior brentuximab unless there was a contraindication to brentuximab.
4. Evaluable disease defined by at least one lesion that can be measured in least 1 dimension and measures at least 1.5 cm in its longest dimension by CT or PET scan, or bone/bone marrow involvement, or skin involvement.
5. No circulating CD5+ malignant cells identified by peripheral blood flow cytometry must be present.

Exclusion Criteria:

1. Pregnant or lactating (nursing) women.
2. HIV infection.
3. Concurrent use of systemic steroids or immunosuppressant medications.
4. Any uncontrolled active medical disorder that would preclude participation as outlined.
5. History of immunodeficiency.
6. History of prior chimeric antigen receptor therapy (CAR T), autologous or syngeneic HCT <100 days from transplant at the time of cell infusion or previous allo-HCT.
7. Active and/or systemic inflammatory or autoimmune diseases.
8. Signs or symptoms indicative of active CNS involvement.
9. Known history or prior diagnosis of optic neuritis or other immunologic or inflammatory disease affecting the central nervous system, and unrelated to lymphoma or previous lymphoma treatment.
10. Clinically apparent arrhythmia, or arrhythmias that are not stable on medical management
11. Current participation in or prior participation in a study of an investigational agent or using an investigational device within 2 weeks of the first dose of treatment.
12. Prior monoclonal antibody therapy within 4 weeks prior to study Day 1
13. Prior use of alemtuzumab
14. Prior chemotherapy targeted small molecule therapy, or radiation therapy within 2 weeks prior to study Day 1
15. Uncontrolled active infection requiring systemic therapy.
16. Circulating CD5+ malignant cells identified by peripheral blood flow cytometry present.
17. Active and/or systemic inflammatory or autoimmune diseases.