After a bit of Googling and looking around the Brother site, I found
http://welcome.solutions.brother.com.../en/index.html It shows how to get the drivers for Linux distributions.
Here is the driver table for the HL-5340D.
http://welcome.solutions.brother.com....html#HL-5340D
Whichever method of installing is your choice. I don't know the difference between cupswrapper or LPR so I can't help you on that one-- I would choose the
cupswrapper one because it's a higher version, though.
For installing the driver, you're on your own since I don't own such a printer but I did manage to find this installation page to help with the cupswrapper install verison.
http://welcome.solutions.brother.com...on_prn1c.html#
and if you chose the LPR version
http://welcome.solutions.brother.com...tion_prn3.html
Best of luck,
True