Hi seitusink,
Welcome to the Apple Support Communities!
The latest version of Safari on Mac OS X 10.6.8 would be 5.1.10. To get a newer version of Safari, you may want to consider updating your operating system. Mac OS X 10.9 is available as a free download from the App Store if your computer meets the System Requirements.
The first article attached here shows the System Requirements for Safari while running Snow Leopard.
Safari 5.1.10 for Snow Leopard
http://support.apple.com/kb/DL1569
The next article here will list the Mac OS X 10.9 System Requirements to see if your computer is compatible with the update.
OS X Mavericks: System Requirements
http://support.apple.com/kb/HT5842
Have a great day,
Joe