On the Swiss Canon support site, I found the driver source code for the PIXMA MG5400. Just scroll all the way down and hit "Akzeptieren & Herunderladen" (Accept and Download).
You'll receive a tar.gz archive containing the source code. Extract it and open a terminal in the directory cnijfilter-source-3.80-1 where you extracted it.
Execute the command chmod +x scripts/install_deb/install.sh, then execute scripts/install_deb/install.sh
The make, make install way doesn't work, as the Makefile is corrupted...
This might do it. However, I don't know how old this is and how well it is maintained.
EDIT: The other answer points to Canon Singapore, which provides a prepackaged version of the driver for Debian: http://support-sg.canon-asia.com/contents/SG/EN/0100467602.html?r=s&q=
Download, extract, and run the installer script.
install.shI get: An error occurred. A necessary package could not be found in the proper location. I think the script is last modified in 2012. Because I seeCopyright CANON INC. 2001-2012– aegyed Sep 22 '14 at 20:05cd scripts/install_deb && ./install.sh– s3lph Sep 22 '14 at 20:06install_debdirectory. – aegyed Sep 22 '14 at 20:07cnijfilter-source-3.80-1I get the same error if i try to execute the isntall.sh from there as well.scripts/install_deb && ./install.shorscripts/install_deb/install.sh– aegyed Sep 22 '14 at 20:15install.shscript, but it failed at a pointcnijfilter-mg5400series depends on libtiff4; however: Package libtiff4 is not installed.I triedsudo apt-get install libtiff4but it is not found in the registry. In system settings -> printers I see Canon MG5400 series with a green tick. I tried a test print, on the printer I sawProcessing... Please wait momentarilythen it disappeared and nothing happend – aegyed Sep 22 '14 at 20:22