iTunes updated my iPhone 5c to 9.1 but now iTunes on my PC wont connect to my phone I have updated my iPhone 5c to iOS 9.1
When I try to connect it to my iTunes Library I get a message that the iPhone can't be used as it requires a newer version of iTunes. 

iPhone and iTunes are both up to date.

I'm using Windows Vista.
Your version of iTunes is unlikely to be up to date [currently 12.3.1], as the latest version requires a minimum OS of Windows 7.

Your only real solution would appear to be to upgrade your OS.


  Windows System Requirements  
  
  Hardware:  
  
  
  PC with a 1GHz Intel or AMD processor with support for SSE2 and 512MB of RAM  
  To play standard definition video from the iTunes Store, an Intel Pentium D or faster processor, 512MB of RAM and a DirectX 9.0-compatible video card are required.  
  To play 720p HD video, an iTunes LP or iTunes Extras, a 2.0GHz Intel Core 2 Duo or faster processor, 1GB of RAM and an Intel GMA X3000, ATI Radeon X1300 or NVIDIA GeForce 6150 or better are required.  
  To play 1080p HD video, a 2.4GHz Intel Core 2 Duo or faster processor, 2GB of RAM and an Intel GMA X4500HD, ATI Radeon HD 2400 or Nvidia GeForce 8300 GS or better are required.  
  Screen resolution of 1024x768 or greater; 1280x800 or greater is required to play an iTunes LP or iTunes Extras  
  16-bit sound card and speakers  
  Broadband Internet connection to use Apple Music, the iTunes Store and iTunes Extras  
  iTunes-compatible CD or DVD recorder to create audio CDs, MP3 CDs, or back-up CDs or DVDs. Songs from the Apple Music catalogue cannot be burned to a CD.
  
  
  Software:  
  
  
  Windows 7 or later  
  64-bit editions of Windows 7 and Windows 8 require the iTunes 64-bit installer; for more information, visit www.itunes.com/download  
  400MB of available disk space  
  Screen reader support requires Window-Eyes 7.2 or later; for information about accessibility in iTunes, visit www.apple.com/accessibility  
  iTunes is now a 64-bit application on 64-bit versions of Windows 8 and 7. Some third-party visualisers may no longer be compatible with this version of iTunes. Please contact the developer for an updated visualiser that is compatible with iTunes 12.1 or later  
  Apple Music, Apple Music Radio, iTunes in the Cloud and iTunes Match availability may vary by country
  


Source: http://www.apple.com/uk/itunes/download/