The PlayStation 4’s games are playable on the PlayStation 5. Here’s how you get them from the former machine to the latter.
By far the best and fastest method is to break out an ethernet cord — remember those? — and start the download using the local network option. You could do it wirelessly, or even upload everything to the cloud and download that to your new console, but that sounds painfully laborious, even if you have a superfast connection.
There are all kinds of other ways — this is a Sony device, after all — including just putting the stuff on a thumb drive and transferring it the old fashioned way. Obviously, if you have your games installed to a third-party external hard drive, just unplug that from the PS4 and put it in the PS5 and you’re set.
Doing just that is the recommended choice, as it frees up the rather limited PlayStation 5 solid-state drive for actual PS5 titles. (My summer quarantine project was putting every PS4 game I own on an external HDD, by the way.)
TL;DR: There are multiple ways to get your PS4 games playing on your PS5, including just taking a disc and installing that to the new console. It might take a while, but you’re covered.