Short answer, no. Looking at your site, you are running TwentyThirteen version 2.1. The current version is 2.5. There are significant changes to the style.css and functions.php files between versions 2.1 and 2.5.
I assume that you want to update the theme to take advantage of the new WordPress 5.0 features. In order to do that properly, you need all the changes provided by version 2.5, including the changes to the style.css and functions.php files. If you were to take the TwentyThirteen version 2.5 files and replace the style.css and functions.php files with your own versions, things will not work or look as expected.
You have three options:
- Continue to use your current theme as-is.
- Switch to a new theme and customize it from scratch.
- Starting with a base of TwentyThirteen version 2.5, re-add the modifications you made to the functions.php and style.css files. This way you can get all the updates of the 2.5 version and still have your custom design.
I should note that you really should learn how to use child themes. Child themes were created to help people avoid these problems.
