Just double click firefox-bin.

This will not update your current install, it will just run from your downloads folder. see screenshot

Ark extracted Version 119 files into /home/Downloads/Firefox/Firefox. I tried ./update from the BASH command line, but didn't know which argument(s) to add to that command. I'm hoping to update Firefox 78.14 ESR to a recent version, whether ESR or not.

The tarball is basically a archive of the full version as you just untar and then run the firefox-bin to use Firefox. There is no installer, make, build, updater, etc.

If the version of Firefox 78 ESR you have is a package build from your distro then the updates are from them if your distro version is still being supported. Mozilla does not update these builds.

There are two ways to update the official builds of Firefox from Mozilla.org like https://www.mozilla.org/firefox/all/#product-desktop-release

You can either check for internal Firefox updates under Help menu in which you would get updates to current 115.8.0esr if it did work. Or you can try to update the hard way with .mar file (only for official build) and not officially supported. https://wiki.mozilla.org/Software_Update:Manually_Installing_a_MAR_file

Or you can just use the tarbal build. Just make sure the Firefox folder has read/write permissions for the user to get internal Firefox updates from Mozilla.

What Linux distro do you use? Is it still supported with updates or has it reached EOL?

Verify that you meet the System Requirements (GTK+ and GLib) for the current Firefox release.

• https://www.mozilla.org/en-US/firefox/system-requirements/
• https://www.mozilla.org/en-US/firefox/123.0/system-requirements/

See also:

• https://support.mozilla.org/en-US/kb/install-firefox-linux
• https://www.mozilla.org/en-US/firefox/all/#product-desktop-release

Yes, what distro and version are you on? Here's my distro version. see screenshot

OK, found "my questions", which I couldn't find in emails received... I'm using Debian Buster, after briefly trying Bullseye. I was hoping to update, but newly installed Firefox 119 will be fine. Do I need to create a link from /home/Downloads/firefox/firefox/firefox.bin to /usr/share/applications/firefox.desktop ? My KDE desktop current Firefox icon properties says "points to" /usr/share/applications/firefox-esr.desktop Thanks again.

Yep, links are what I have on my KDE desktop. Your current install Firefox path will be different.

You should give openSUSE Tumbleweed a try.  ;-)) Try running a live usb stick. https://en.opensuse.org/SDB:Live_USB_stick

To answer James' question, 78.14 ESR was installed from the Buster installation 2 years ago. And, cor-el, I don't know if Buster is still supported. I made a DVD of Bullseye, but then changed back to Buster. Firefox 119 already seems to have upgraded itself to Firefox 123, but it's working fine. I added a KDE Destop link to it, but couldn't seem to add it to KDE's start menu. I'll ask a question on linuxquestions.org, if I have time. Thanks for all answers.

I would just pin it to the task manager for a wee bit faster access.