Processively dephosphorylates Ser-5 of the heptad repeats YSPTSPS in the C-terminal domain of the largest RNA polymerase II subunit (rpb1). 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. Ssu72 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, which is composed of cft1, cft2, ysh1, pta1, swd2, pfs2, dis2, yth1, ssu72, and fip1. Belongs to the SSU72 phosphatase family.