First of all, the manufacturer will boast that its latest hardware is compatible with the most recent socket release, so you'll find the information from wherever you purchase your cooler. You're looking for "AM5" under "Socket support" or something close to those words.
If you have an older CPU cooler and outdated information, then AMD has you covered here too. Most AM4 coolers are forward-compatible with AM5. So this in essence means the upgrade from AM4 to AM5 should be seamless in terms of coolers. But as you will see below, it's not that clear cut, as some AM5 coolers struggle to cool the 253W TDP titans.