You are not running an intel mac with OSX 10.5 Leopard. Unfortunately, Mac's Java 1.6 is only designed for 64-bit computers such as their newer intel macs. And LW 5 requires Java 1.6.
Don't fear. You can get an older version, not that old. And btw LW 4 is actually much better than the present LW 5 anyway.
Since you have installed LW 5, what I suggest you do is move the LW program to the trash. Then you will need to remove the
install limewire.pkg file to the trash also, otherwise the system will not let you install an earlier LW version. See more about it here
http://www.gnutellaforums.com/mac-os...0-5-later.html