How do I fix network error 1001 when updating iTunes or macOS on iMac?

You can find links to iTunes documentation and downloads here: iTunes for Mac Manuals and Downloads - Apple Support

You may or may not be able to connect to the Apple download server with the old iMac. If you cannot, then you may be able to connect and grab an installer with a newer machine and transfer that to the old with a flash drive.

NORM-FWF wrote:

Hi there I have bought a new iMac running osx 10.5.4

If it is running 10.5.4 (Leopard), it is far from new. The most recent iMacs that were able to run Mac OS X 10.5.4 were ones released in Early 2008!

Perhaps you meant macOS 15.4 (Sequoia)?

I want to use it to restore iPods and it says I need to update iTunes

Apple got rid of the Mac version of iTunes several years ago, breaking up its functions among several applications (Music, TV, Podcasts, Books) and the Finder. You use the latter four applications to manage your media libraries – and the Finder to manage portable devices (iPhones, iPads, iPods) and handle manual synchronizations to them.

Sync your iPhone, iPad, or iPod using your computer - Apple Support

That's going back a bit...

iTunes (the app) was retired in 2019 in favor of Apple's Music app, so that's where Music is now managed. So that would be the place to start. Does the iPod appear in the Music sidebar?

The hardware and software you are using, including the iPods themselves, are so obsolete now; the only way you will get this to work is some kind of custom hack you incorporate which disables the update requirement. Probably not worth any of that effort unless you are doing this as some kind of business, in which case, you'll need to find and hire an expert who specializes in obsolete hardware and software.

Cheers