To my knowledge LW 5.5.16 does not work/connect these days. Unless you have a version that was hacked somehow.

Unless you disagree, may I suggest this LW 5.6.2 Pirate Edition: Hotfile.com: One click file hosting: LimeWirePirateEdition_Win.zip

(Versions of LW between 5.5.9 to 5.5.16 did not have any program improvements. All changes were in regard to auto-updating and preventing you using/connecting with the program.)

For Windows 7, you need to have the Java set to 'Run as Administrator' or else there will probably be connection problems. Search your computer for Java.exe, once you find it in search results, right-click the Java.exe in search results and choose Properties, Compatibility tab, check the option that says, 'Run this program as an Administrator' and press Apply and OK.

And use a fresh connection fix. LPE ConnectFix (updated today)

If still connection problems post back.