iTunes 10.7 requirements
• Mac computer with an Intel Core processor and 512MB of RAM
• To play 720p HD video, an iTunes LP, or iTunes Extras, a 2.0GHz Intel Core 2 Duo or faster processor and 1GB of RAM is required.
• To play 1080p HD video, a 2.4GHz Intel Core 2 Duo or faster processor and 2GB of RAM is required.
• Screen resolution of 1024x768 or greater; 1280x800 or greater is required to play an iTunes LP or iTunes Extras
• Broadband Internet connection to use the iTunes Store
• Apple combo drive or SuperDrive to create audio, MP3, or back-up CDs; some non-Apple CD-RW recorders may also work
• Apple SuperDrive to back up your library to DVDs; some non-Apple DVD-RW drives may also work
• Mac OS X version 10.6.8 or later
• Safari 4.0.3 or later
• 350MB of available disk space
• iTunes in the Cloud and iTunes Match availability may vary by country.
As you see, you need to upgrade your OSX.
you have 10.5.8
Don't upgrade right away, check the hardware specs first.