Hi Kathy and Welcome. My Name is ***** ***** I look forward to assisting you today with your question.
You need to upgrade to latest OS X to get latest Safari. If you are on latest OS X, it won't ask you to upgrade.
To get the latest version is Mac OS X 10.11 El Capitan. To get the latest OS X, click on the Apple icon and select App Store. This will bring App Store. In App Store, click on Updates. Do you see OS X El Capitan there ? If so, click Free Upgrade and let it download it. Then install it.
Or click on Featured tab and you will fine OS X El Capitan on right side. Click on it and download it.
Or download it from here --> https://itunes.apple.com/in/app/os-x-el-capitan/id1018109117?mt=12
El Capitan is a big file, so it will take a while to download and install.
Please let me know if that didn't work, so we can continue troubleshooting.
If you want, you can switch to another browser like Google Chrome. Chrome is batter than Safari and it will work with all websites out there without any problems. You can download Chrome from here --> https://www.google.com/chrome/browser/desktop/
Or you can upgrade your OS X using my previous instructions.