Final answer:
The proofreading activity of bacterial DNA polymerase-I resides in the 5'→3' exonuclease domain, while for DNA polymerase-III, it's in the β' subunit.
Step-by-step explanation:
The proofreading activity of bacterial DNA polymerase-I resides in the 5'→3' exonuclease domain of the enzyme. This domain is removed by mild protease treatment, leaving behind the large fragment called the Klenow fragment which has the polymerization and proofreading activity.
For DNA polymerase-III, the proofreading activity resides in the β' subunit. This subunit is responsible for removing mismatched nucleotides during DNA synthesis, thus ensuring accuracy in DNA replication.