Export your tables using phpmyadmin interface. Just select those tables only that you want to export from the old database and import those tables in the new database
or you can run the command(query) in mysql to copy one table
create table newdbname.newtablename like olddbname.oldtablename;
INSERT INTO newdbname.newtablename SELECT * FROM olddbname.oldtablename;
Repeat the same command to copy other tables