Upgrading OS X from 10.5.8 to at least 10.6.8 to update my iTunes Recently purchased an iPhone 5c and was trying to upload my music and apps from iTunes. iTunes could not upload music because iTunes needs to be at least 10.6.8 to update. On my 2006 iMac I am currently running OS X 10.5.8, therefore I can not update my iPhone 5 with music and apps.

Reading your response from a similar case what would be the process of updating my OS in order to update my iTunes? And is it even feasible considering my iMac is pretty old? 
Below is my Hardware Overview. The computer runs strong, but I hear from others (don't know if I can trust) that it's time to upgrade my iMac but I am trying to avoid buying a new iMac if I can.

Processor Name: Intel Core Duo
Processor Speed: 2 GHz
Number Of Processors: 1
Total Number Of Cores: 2
L2 Cache: 2 MB
Memory: 1 GB
Bus Speed: 667 MHz
Boot ROM Version: IM41.0055.B08
SMC Version (system): 1.1f5
According to Apple Support page your mac is capable of running Mac OS X 10.6 Snow Leopard.

General requirements

Mac computer with an Intel processor
1GB of memory
5GB of available disk space
DVD drive for installation
Some features require a compatible Internet service provider; fees may apply.


Also considering Apple policy in supplying security updates, I would recommend you to update (all the care in taking backup of your documents apply). 
At this page there is a list of security updates, and the last one for 10.5 was in 2012.