Contributes to degradation of proteins cross-linked by transglutaminases by degrading the cross-link between a lysine and a glutamic acid residue. Catalyzes the formation of 5-oxo-L-proline from L-gamma-glutamyl-L-epsilon-lysine. Inactive with L-gamma-glutamyl- alpha-amino acid substrates such as L-gamma-glutamyl-L-alpha-cysteine and L-gamma-glutamyl-L-alpha-alanine. . This is the function of GGACT (gamma-glutamylamine cyclotransferase, ENSG00000134864).