For us on Ubuntu 12.10 it wouldn't print anything (not even the test page) and would blink red/orange the bottom 4 lights when we tried to print. We resolved it by switching drivers to a generic driver (the Linux ones listed on Brother's website didn't appear to work, maybe I messed up the install) and even double-side printing works now! Ubuntu seems to recognize the printer and automatically add using the Br-Script3 driver.
To change it, since I have Cinnamon, I went into cinnamon-settings
(gnome-control-center
does NOT appear to let you change the driver associated with an automatically recognized printer), Printers > HL-5340D right click, Printer Properties > Settings, Make and Model, Change > Select Printer from Database, Generic, Forward > PCL 6/PCL SL > Generic PCL 6/PCL XL Printer -CUPS+Gutenprint v5.2.9.
I have included a screenshot of the appropriate settings. Cinnamon Settings is what you want, on the left/bottom. Gnome-control-center on the right doesn't work.
Edit: my friend got it to work without Cinnamon by
going to localhost:631
and then roughly do the same procedure (select the printer, Administration > Modify Printer, ...).