Eagle 5.6 depends on libjpeg6 to run. I case you have upgraded to libjpeg7 there are a few tricks to help you run eagle.
One trick you should not use though is to make a libjpeg6 link, linking to libjpeg7. This could possibly mess up other application on your system.
Install libjpeg6 from AUR.
If you don’t want to install libjpeg6 sytem-wide there is a more elegand way to fix it: 1. grab a copy of libjpeg6 2. put it somewhere inside your home directory or for example inside /opt/eagle/lib 3. edit the launcher script (/usr/bin/eagle) and add before the exec ./eagle command:
Grab eagle from AUR.
Update: as of 5.6.0-2 version in aur, you do not need to do the above steps as the PKGBUILD will take care everything for you.