Upgrading OS X from 10.5.8 to at least 10.6.8 to update my iTunes
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.