Does anybody know if that will work ?

I need to upgrade the OS > to upgrade Safari > to upgrade I-Tunes > to use the I-Tunes Store....

But only 10.5.5. is official supported with MC 3.1.3.

If you will look/search you will find a couple of threads with other users' experiences with 10.5.7.  I have run 10.5.7 and am currently running 3.1.3 on 10.5.8 with no problems on my Mac Pro 2.8 eight core with Quicktime 7.6.2.  As always, you run the risk of having problems with an unsupported version of the OS software, so I would advise making a complete backup and cloning your drive if you have problems so you can put things back to the way you had them easier.  I would also advise downloading the Combo update for any OS X update instead of using Software Update.  Repair permissions prior to installing and immediately after installing any updates.  It might not hurt to uninstall then reinstall the Avid software after updating the Apple Software.

OK, thank you.