Browsers compatible with an early 2009 iMac

The problem is not the browser, it's the OS. Browsers can only run on those OS versions that are designed for it and Firefox has been around for a very long time.

If the browsers are out of date, I.e security is lacking, you need to upgrade your OS. That may mean a new, or newer, Mac.

A 14 year old Mac has had a good run, but it's time to consider replacing it.

To add a bit to ku4hx's reply, today's secure (https) websites require, at least, the TLS 1.2 security protocol to access them. Apple did not include this protocol until OS X 10.9 Mavericks & Safari 7.0. Prior to this, OS X only supported SSLv3 & TLS 1.0. This shouldn't be the issue since your iMac is running macOS 10.11.

You can test your browser's SSL/TLS capability at this link: TLS test for web browsers - howsmyssl.com

Ref:

• Requirements for trusted certificates in iOS 13 and macOS 10.15 - Apple Support
• If Safari says it can't establish a secure connection, or the website is using weak encryption - Apple Support (archive)

thank you very very much. the only thing dad goes on iMac is watch films and news. i have given him a browser option. Failing that i did get him an iMac for Christmas its a little newer than the 2009 but only by a couple yrs only as it was given to me via my IT tutor job.

i have a Macbook Pro 17" 2011 so i guess my browsers need updating too.

thank you all

this guy made a list Browsers by Mac operating system - Apple Community