My older Mac uses OS 10.12.5 and Safari version 10.1.1

If your computer can run 10.12, it can run 10.13, which would let you upgrade to Safari 13. If the upgrade installs Safari 12, you might want to stick with that instead of upgrading Safari to version 13. You can look at the Safari community to see the problems people are having with version 13.

How to get macOS High Sierra   

Check to make sure your applications are compatible.      

Application Compatibility

Also check to make sure there is a compatible driver for your printer.

Do a backup before installing, preferable 2 backups on 2 different drives.

You are welcome. If you are now using High Sierra, you can check the App Store for a Safari upgrade. I personally wouldn't upgrade Safari to version 13. Based on what I have read in the Safari community, version 13 has a lot of bugs in it.

Thanks for the information macjack . I am still reluctant to use Safari 13 based on what I've read. I realize the Support Community is the 'emergency room' and many others are using it without any problem, but having 4 updates already when Safari 12 only had 2 updates in a year, seems to indicate it wasn't properly tested before release.

You are welcome. That is fairly slow. Did the download finally finish? There is a link in the article I posted if you need to try again.

FWIW I'm running Safari 13.0.4 in High Sierra with no issues. I've also upgraded Safari through all the 10.13 versions so far with no issues.

You are welcome.

Eric Root wrote:

4 updates already when Safari 12 only had 2 updates in a year, seems to indicate it wasn't properly tested before release.

That's nothin'! Do you use an iPhone? 😎

Just an iPad and it is too old to update to IOS 13. 😱