Catalyzes the cleavage of 5-oxoproline to form L-glutamate coupled to the hydrolysis of ATP to ADP and inorganic phosphate. 5-oxo-L-proline + ATP + 2 H2O = ADP + H(+) + L-glutamate + phosphate Forms a complex composed of PxpA, PxpB and PxpC. Belongs to the LamB/PxpA family.