Metallocarboxypeptidase that mediates deglutamylation of tubulin and non-tubulin target proteins. Catalyzes the removal of polyglutamate side chains present on the gamma-carboxyl group of glutamate residues within the C-terminal tail of alpha- and beta- tubulin. Cleaves alpha- and gamma-linked polyglutamate tubulin side- chain, as well as the branching point glutamate. Also catalyzes the removal of alpha-linked glutamate residues from the carboxy-terminus of alpha-tubulin. Mediates deglutamylation of nucleotidyltransferase CGAS, leading to CGAS antiviral defense response activation. . This is the function of AGBL5 (AGBL carboxypeptidase 5, Ensembl gene identifier ENSG00000084693).