I need to update my Safari for my desk top now

See if you can upgrade to 10.12, 10.13, 10.14, or 10.15, see sys requirements...

https://support.apple.com/kb/sp742?locale=en_US

https://itunes.apple.com/us/app/macos-sierra/id1127487414?ls=1&mt=12

https://support.apple.com/kb/sp765?locale=en_US

https://itunes.apple.com/app/macos-high-sierra/id1246284741?mt=12

https://support.apple.com/kb/SP777?locale=en_US

https://itunes.apple.com/us/app/macos-mojave/id1398502828?mt=12

macOS Catalina - Technical Specifications

General Requirements

▪ OS X 10.9 or later

▪ 4GB of memory

▪ 12.5GB of available storage (OS X El Capitan 10.11.5 or later)*

▪ Some features require an Apple ID; terms apply.

▪ Some features require a compatible internet service provider; fees may apply.

Mac Hardware Requirements

For details about your Mac model, click the Apple icon at the top left of your screen and choose About This Mac. These Mac models are compatible with macOS Catalina:

▪ MacBook (Early 2015 or newer)

▪ MacBook Air (Mid 2012 or newer)

▪ MacBook Pro (Mid 2012 or newer)

▪ Mac mini (Late 2012 or newer)

▪ iMac (Late 2012 or newer)

▪ iMac Pro (2017)

▪ Mac Pro (Late 2013 or newer)

https://support.apple.com/en-us/HT210190

How to upgrade to macOS Catalina – Apple Support

And caution on 10.15, to see which Apps will no longer work in 10.15 get Go64...

https://www.stclairsoft.com/Go64/

No. The latest version of Safari, Safari 13.0.5, requires macOS High Sierra or newer. The latest version of Safari available for OS X El Capitan is Safari 11.1.2.

Because Safari 11 is relatively outdated, I would recommend updating your iMac to macOS High Sierra or newer for better security.

Since you have a higher OS version than I do, but I have a higher Safari version (with a lower OS) than you do, the only thing I can suggest is to reinstall High Sierra; hopefully that would include the latest Safari version for your OS.

that depends on whether your Mac can be upgraded. What is the exact year, model?

Lanney, anything working for you?

how do i update safari on this computer

Safari is tied to the OS version for the most part/

Try this browser...

https://brave.com/

I need to upgrade to safari 12 , which is not a option on app store, i currently have macOS high sierra version 10.13..5

You say you need Safari 12 and you are on High Sierra 10.13.5?

Well, you should check your Safari version because I have Sierra (10.12.6) and my Safari version is 12.1.2.

my safari version is 11.1.1