To be able to sync the music from your iPhone or download any purchased music you purchased on your iPhone via your Mac?
No.
All music is purchased through iTunes. You could try the version of iTunes you have now on your Mac to see if any of your newly purchased music and iOS Apps can be downloaded to you Mac, but you will NOT be able to sync your iPhone at all to get any data or info off of if into iTunes
One way to get pictures off of your iPhone is to email them to yourself and/or try to find a cloud service, like DropBox, that will still be compatible with your version of OS X and a version that is on the App Store for iOS and use this from your iPhone to get info to your Mac.The Mac version has to work with OS X 10.5 Leopard to be able to work back and forth between your iPhone and Mac.
You will have Google for this as I have no idea if there are any cloud services available that will work with a Mac running OS X 10.5.8 Leopard.
This OS X version is very old and many developers have abandoned support for this OS X version.
No newer versions of OS X will not work or be downloadable as these only work with newer Intel CPU Macs and all version of OS X from OS X 10.7 Lion and forward are download only, now, from the Mac Apps Store which is only available from Mac OS X 10.6.7 Snow Leopard onward and OS X 10.6 Snow Leopard is for newer Intel Macs and WILL NOT work on older PowerPC Macs like yours.
Other than the alternatives I gave you, a new or newer (used) Intel Mac are your only options.
Your Mac is just too old ( almost 10 years old).
Sorry,
Good Luck!