What is the best way to resurrect and update my old WordPress site?

I had an old WordPress site that was neglected for several years. It had been hacked, and I disabled it. I’d like to now get it back up and running with the latest version (5.5.1).

I see from the version.php file that it was running WordPress version 4.5.16, and $wp_db_version was 36686. From what I can tell, the database does not have any corruption in it, just the old files. I have set up a new area for the website on a fresh server. My question is: Should I install the latest version right away and connect it to the old database data, or would it be better to download a fresh, uncorrupted copy of version 4.5.16, get that working, and then update it to the current version? Is there anything in the database from the old site that will give me problems if I try to run 5.5.1 without going through the update process? If I go straight to 5.5.1, will the software automatically update the database itself somehow?

Further explanation:

The site, where it was, is disabled; I will not be logging into the old site. What I do have is all the files and the database backed up. My question is: When I put this on a new server and get it back up and running, should I use the old WordPress core files (or better yet, download a fresh copy of 4.5.16), get that working with my database, and then update everything to the latest version? Or would it be better to skip that step, install the latest and greatest WordPress core files, and restore my old database in that?

As far as user content goes, the theme was a child theme for TwentyTen that I wrote myself; I will take care of restoring that and making sure it is updated and secure. The only other content files are images that I can restore. My question is specifically about which version of the WordPress core files I should connect to the database first.

PHP version: On my new server, the oldest PHP version I can run is 7.2. Would I even be able to run and update WP 4.5.16 under PHP 7.2?