My bank does not support quicken 2005 because of the filetype change. 
My bank will, however, allow me to export my transaction information
to a CSV file. My question is, can I import this CSV data into Quicken
2005?

I have the same problem - kinda.  I lost some transactions by moving
computers and now I have a few months gap in my quicken.  I can get
PDF files of my statements so I wrote a perl script that converts this
to qfx format.  Quicken seems to need an web connect account to make
this work.  Arrrgh!  I just want to import some data!  They made
things a lot harder on people by elmination their old import
abilities.