Efficiently catalyzes the hydrolysis of the 3'-phosphate from 3',5'-bis-phosphonucleotides as well as the successive hydrolysis of 5'-phosphomononucleotides from the 5'-end of short pieces of RNA and DNA, with no specificity toward the identity of the nucleotide base. Is more efficient at hydrolyzing RNA oligonucleotides than DNA oligonucleotides. This enzyme can also hydrolyze annealed DNA duplexes, albeit at a catalytic efficiency lower than that of the corresponding single-stranded oligonucleotides. a ribonucleoside 3',5'-bisphosphate + H2O = a ribonucleoside 5'-phosphate + phosphate Belongs to the PHP family. TrpH/YciV subfamily.