If you want to try & get LW 5 working, start off by reinstalling/updating Java. Download the JRE (Java Runtime Environment) offline installer: Java SE Downloads - Sun Developer Network (SDN)
Remove any other Java versions installed via Control Panel, then install the latest Java, then restart your computer.

Otherwise there are more fixes here: http://www.gnutellaforums.com/333278-post2.html

If nothing works then you can always keep using an older version of LW (providing that it's not too ancient). There's info here about downgrading, plus a link to download an earlier version of LW if you don't have any old installers saved: Downgrading to LimeWire 4 from 5 & resuming incomplete downloads