The Civics of that era are not listed in the dinghy towing guides and the 2005 owner's manual will not give any instructions or mention "recreational towing" at all. It was around that time period when Honda started to discourage any of their vehicles from being flat towed with the exception of the CR-V.
However, many are flat towing Civics of that age with both automatic and manual transmissions without issue.
Take a look at this thread from 2006, specifically the posts from
Gary RVRoamer and
Tom N or posts
#3 and
#5 for the actual procedure.
'03 Honda Civic Flat Towing
Also, look at these threads too that you'll find interesting:
Honda Civic Towable?
Can I tow my 2004 Honda Civic Auto Trans.