I have a late 2012 IMac with OSX10.9.5, 2.7GHz i5. On many websites including Yahoo Mail it tells me I need to update Safari or use a different updated browser. I've received no updates for Safari from Apple in a long time. My question is how do I update Safari? I have downloaded Google Chrome but do not use it as my default browser.

As far as I've been able to tell, the only way to update Safari is to install a newer version of Mac OS than what you have. Of course that is not possible when your Mac isn't supported by the latest Mac OS X.

Mac OS 10.9.5 is old now. 10.14 is the current one, and it doesn't support some older Macs. People have found that out the hard way when they tried to install OS 10.14 on their older Macs and got a non-functional computer.

This site tells whether your Mac can run OS 10.14
https://coolestguidesontheplanet.com/minimum-system-requirements-for-macos-mojave-10-14/

The only thing you can do is to choose another browser that isn't tied to the OS version. If you don't like Chrome, you can try Opera. I wouldn't recommend Firefox until they fix their current problem with certificate expiration (supposedly that should be soon). There are also browsers like Seamonkey and Vivaldi that have Mac versions. You can check a list of other browsers here
https://en.wikipedia.org/wiki/Comparison_of_web_browsers

Thanks Jenny for looking into this for me. I will check out the sites. I appreciate your taking the time to research it for me.