It's really an upgrade that's necessary, not just an update.
The next OS X up from v10.5.8 is Snow Leopard.
Check the requirements here > Mac OS X v10.6 Snow Leopard - Technical Specifications
If your Mac meets those requirements, you can purchase Snow Leopard from Apple > Mac OS X 10.6 Snow Leopard - Apple Store (U.S.)
That will automatically update Safari for you but keep in mind, Snow Leopard is an older OS X. you may not be able to use all of Safari's features.
With Snow Leopard v10.6 installed, you may be able upgrade to OS X Lion. Requirements > OS X Lion - Technical Specifications
This appears to be the last Safari update for OS X Leopard.
Microsoft sells Word for Mac. Check with MS for the availability for the version that runs on Leopard.