Which Linux distribution would suit an older laptop and a beginner?

There isn’t one universal beginner distribution. The best choice is usually the one whose desktop feels comfortable and that you’ll use regularly. If you’re interested in eventually learning system administration or DevOps, Fedora or Ubuntu can be useful later, but starting with Mint is perfectly reasonable.

Linux Mint is usually my first recommendation for someone new to Linux. It’s polished and easy to use without forcing you into an especially complicated setup. Your laptop is more than capable of running it, and you can gradually customize things as you learn.

A PS5 controller will often work, but its setup can be less straightforward than with an Xbox-style controller because of driver and Bluetooth differences. Keyboard-only use is generally fine, and many desktop environments let you navigate menus and launch applications without a mouse. For a lighter desktop, Lubuntu is worth considering, although your hardware can handle most mainstream choices.

Fedora with the KDE Plasma desktop could be a good middle ground. It has relatively current software and plenty of customization, while still being approachable. KDE also supports extensive keyboard navigation and controller configuration.

Your laptop isn’t particularly weak, so you don’t need to limit yourself to lightweight distributions. You could make a USB drive with several installers and boot them in live mode to test the desktops before installing anything. Mint, Fedora KDE, Kubuntu, Pop!_OS, and Lubuntu would all be reasonable ones to try.