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What version of Mac OS X are you using ?
Safari 5.1 is the latest Safari version that 10.6 Snow Leopard can handle. To update into latest Safari, you have to update the OS X into latest OS X version first. The latest OS X is 10.11 El Capitan.
On your Mac, open the App Store application from Applications folder. Then search Mac OS X or click OS X El Capitan. Install Mac OS X El Capitan from there. If you are using any third party applications like Adobe, Quark etc then let me know before updating the OS X. El Capitan is free. You can download and install it now from App Store for free.
If you don't want to update to latest OS X, then you install latest Firefox or Chrome. Chrome or Firefox browsers are far better than Safari.
Download Chrome from here --> https://www.google.co.in/chrome/browser/desktop/
Download Firefox from here --> https://www.mozilla.org/en-US/firefox/new/
If you have any questions or would like any additional information, please don't hesitate to ask.