What are the OS X Mavericks hardware system requirements?
System requirements can be found at Apple - Upgrade your Mac to OS X Mavericks. Click the View compatible Mac models link under the Check your Mac hardware step to view the supported models.  Currently:


  Mac models compatible with OS X Mavericks 
  
  
  iMac (Mid 2007 or newer)
  MacBook (Late 2008 Aluminum, or Early 2009 or newer)
  MacBook Pro (Mid/Late 2007 or newer)
  MacBook Air (Late 2008 or newer)
  Mac mini (Early 2009 or newer)
  Mac Pro (Early 2008 or newer)
  Xserve (Early 2009)
  


From the Apple menu select "About This Mac" and then click the "More Info…" button to determine exactly what model you have.

According to the information at How to identify iMac models, the iMac5,1 is the Late 2006 model, which is not compatible with OS X Mavericks.