Need iTunes 10.5 for Windows XP 32-bit

Are you sure you need iTunes 10.5?

That's an incredibly old version. Windows XP could install iTunes 12.1.3.6

The following User tip has links to older versions of iTunes but does not go back to iTunes 10.5.

click here ➜ Troubleshooting issues with iTunes for Windows - Apple Community

I have iTunesSetup 10.6.3.25.exe dated 19/8/2012 if that's any good to you.