Sure, no problem. I have Tele Atlas data here, and the zip code sdc file is named zip5.
-Open ArcMap, use the 'Add Data' button add zip5.sdc from wherever it is on your hard drive.
-Use the Selection tool or open the attribute table and write a query to select features by attributes to choose the zip codes you're interested in.
-Right click the Zip5 layer and choose 'Data' > 'Export Data' in the popup menu.
-The Export Data dialog will appear, .shp is chosen by default so just pick an export location and you should be all set.
Let us know if you have more questions.
Hmm, not sure exactly why it wouldn't export all fields. You mention 'esri_zip5.sdc' and population counts in the fields. The data we're using is available with ArcLogistics or Esri Data & Maps has a 'zip5.sdc' file and only a few fields including Name, FIPS codes, and the Zip code.
Perhaps you have some other file that is in some way protected or licensed?