Hi and Welcome. My Name is ***** ***** I look forward to assisting you today with your question.
You have two options in here. You can either upgrade the OS X to latest 10.11 El Capitan (which will give latest Safari) if your Mac can handle it or you can install another browser Mozille Firefox and you will be able to open that tax website in Firefox.
To upgrade to latest Safari, you need to upgrade the current OS X to latest version. The latest OS X is 10.11 El Capitan. Upgrading to El Capitan also update Safari and other browsers.
Follow the steps below to upgrade the OS X if your Mac support it.
Click on the Apple icon and App Store. This will bring App Store. Click Updates tab. If your Mac can handle latest OS X, then you will see Mac OS X El Capitan there with FREE UPGRADE button. Click Free Upgrade and enter your Apple ID and password.
This will download the update. It may take a few hours to download. Once the download is completed, it will bring the OS X Installer. Follow the onscreen instructions to install it. It may take up to 3 hours to install the upgrade.
If you are unable to upgrade to latest OS X, then just download and install and use Mozilla Firefox -->
Firefox is an alternate browser to Safari and Firefox will allow you to open any websites that Safari doesn't support.
If you have any difficulty on following the steps above, please let me know and I will continue to help you.