Does this happen to all of your downloads, or just a few? Does it happen with audio & video downloads? Or just with one type? Are you downloading torrents?

Do you see the 'stalled' message in the download tray, or does the download just sit there & do nothing?

Have you tried doing a new search for the file? Don't cancel the download (or the file will be deleted completely) - when a download gets stuck, search again for that same file... that's worked for me before with a stalled download.

What version of Java do you have installed? Did you update Java when you installed LW 5?
Try updating to the latest Java. Go to the link here Java SE Downloads & download the JRE offline installer. Remove all other Java versions installed on your computer via Control Panel. Next, install the version that you've just downloaded. Restart your computer.

And if that doesn't help, try installing this older version of Java (JRE 6u5): Archive: Download Java Platform Standard Edition (Java SE) 6u5
Remove your current version before installing this one.

What performance options do you have checked in LW's tools > options > advanced > super really advanced > performance? See whether disabling Ultrapeer, Mojito & TLS makes any difference.