You don't even need to complete the SS-5 when applying in person. The SSA office will enter your info into the computer and printout an application for you to sign.
https://secure.ssa.gov/apps10/poms.nsf/lnx/0100202001RM 00202.001 Form SS-5 (Application for A Social Security Card) - Overview
C. Policy - Types of Applications
An SSN application can be the Form SS-5, the Internet version Form SS-5, or the systems-generated application which collects the same information from the applicant as is obtained on the paper Form SS-5. While any of these formats are acceptable,
you must use the systems-generated application whenever the proper applicant remains in the office throughout the interview and input process. -----------------------------------------------------------------------------------------------------------------------
FYI
https://secure.ssa.gov/apps10/poms.nsf/lnx/0100202115RM 00202.115 Form SS-5 Item 3 — Citizenship
B. PROCEDURE - ANSWER TO ITEM 3
2. Legal Alien Allowed to Work
The applicant should check this block if he/she alleges to be a lawfully admitted alien with work authorization.