Transfer ipod to New computer

There are a number of third party utilities that you can use to retrieve the music files and playlists from your iPod. You'll find that they have varying degrees of functionality and some will transfer movies, videos, photos, podcasts and games as well. Have a look at the web pages and documentation, this is just a small selection of what's available, they are generally quite straightforward. You can read reviews and comparisons of some of them here:
Wired News - Rescue Your Stranded Tunes
Comparison of iPod managers

TuneJack Windows Only
iPod2PC Windows Only
iGadget Windows Only
iDump Windows Only
SharePod Windows Only
iPodRip Mac & Windows
YamiPod Mac and Windows
Music Rescue Mac & Windows
iPodCopy Mac and Windows
iRepo Mac & Windows (iPhone and iPod Touch compatible)
iPod Access Mac & Windows (iPhone and iPod Touch compatible)

If you have any iTunes Music Store purchases the transfer of purchased content from the iPod to authorised computers was introduced with iTunes 7. You'll find details in this article: Copying iTunes Store purchases from your iPod or iPhone to a computer

Has anyone heard of the rumor that you can only sync your ipod in 5 different computers before it fails?

Don't know where you heard that, but it's complete nonsense.

You can sync an iPod to an unlimited amount of computers.

There is a maximum of 5 authorized computers for downloading music purchased from the iTunes store though, and a lot of people confuse the two.