My 2015 iMac will not load websites

Some websites may require a later version of Safari than what is available on High Sierra. To upgrade Safari you need to upgrade the macOS.

The model year of an iMac is available at Apple menu > About This Mac.

A late 2009 through mid 2011 iMac can be upgraded to High Sierra 10.13.6 but no later version. 

A late 2012 through late 2013 iMac can be upgraded to Catalina 10.15.7 but no later. 

A mid 2014 and late 2014 iMac can be upgraded to the latest version of Big Sur macOS 11 but no later. 

A late 2015 iMac can be upgraded to the latest version of Monterey macOS 12 but no later. 

A 2017 iMac can be upgraded to the latest version of Ventura macOS 13 but no later. 

For all of the above, see instructions in: How to download and install macOS - Apple Support  

A 2019 or later iMac can be upgraded to the current version of Sonoma macOS 14. See:How to upgrade to macOS Sonoma - Apple Support

Be aware that if you upgrade to Catalina 10.15 or later you will also need to update any non-Apple 32-bit apps. See: https://www.stclairsoft.com/Go64/

or

 https://www.macworld.com/article/232735/how-to-check-if-mac-software-is-32-or-64-bit.html

If you can’t or don’t want to upgrade, you may want to use a 3rd party internet browser that supports running their current version on your Mac. One option is Chrome: https://www.google.com/chrome/

 There is also a user tip about which browsers will work with each operating system: Browsers by Mac operating system - Apple Community