Processively dephosphorylates Ser-5 of the heptad repeats YSPTSPS in the C-terminal domain of the largest RNA polymerase II subunit (rpb-1). Component of the cleavage and polyadenylation factor (CPF) complex, which plays a key role in polyadenylation-dependent pre-mRNA 3'-end formation and cooperates with cleavage factors including the CFIA complex and NAB4/CFIB. Ssu-72 is required for 3'-end formation of snoRNAs (By similarity). H2O + O-phospho-L-seryl-[protein] = L-seryl-[protein] + phosphate H2O + O-phospho-L-threonyl-[protein] = L-threonyl-[protein] + phosphate Component of the cleavage and polyadenylation factor (CPF) complex. Belongs to the SSU72 phosphatase family.