I have the same issues as you (also using Limewire 5 on 10.5 Leopard);
Limewire freezes, says there is no connection to the Internet (is there no "connect/disconnect" button like there used to be?) does not shut down fully and is still indicated as open on my dock, (even using Force Quit, I sometimes have to Restart my computer to get things going again!)...also, what I find really annoying is that after downloading a file nearly to the end it suddenly says "Corrupt file" and no other option but to "Remove" - if I search for the same file using Limewire 4 on my older Mac, the file downloads no problem no indication of being corrupt! What can I do to continue downloading anyway?
Also, once I shut down and open again without having removed the "Corrupt file" it then says "There is a disk problem" instead. Weird!
Any suggestion on how to debug this are REALLY APPRECIATED!!!

I've found logging out is a much quicker way to make it disappear from the dock. I've also had the corrupt file problem before, it really sucks