That enzyme is DNA Polymerase III (Pol III). Three activities are associated with DNA polymerase I;
5' to 3' elongation (polymerase activity)
3' to 5' exonuclease (proof-reading activity)
5' to 3' exonuclease (repair activity)
The second two activities of DNA Pol I are important for replication, but DNA Polymerase III (Pol III) is the enzyme that performs the 5'-3' polymerase function.