I've not tried it personally, however if you follow the link http://www.eserviceinfo.com/downloadsm/36127/Brother_MFC5840_5440.html
You can download the service manual, there are 5 parts to it, each has to be downloaded seperately.
Another cure I've read is that you get hold of a can of Air Duster, remove the ink cartridge then squirt a blast of air down the ink feed pipe, it's claimed that this will clean the printhead, but will use up ink!
Chris Buckle
April 2009