I had the same problem opening Limewire 5 with my iMac with Intel core 2 duo, running 10.5.6. It was still using the default 32-bit Java, so I went to the MacintoshHD>Utilities>Java>Java Preferences. I saw that Java SE6 was in the list, but not at the top. It must have previously been downloaded during a software update, but was not the Java in use. I dragged Java SE6 to the top of the lists for both the applet versions and application versions.
I downloaded Limewire 5 again and it worked. What a relief.