Since Emagic was acquired by Apple, this specific version represents one of the last major releases before the software became the Mac-only "Logic Pro" we know today. Where to Find It
I can help with tips on finding a compatible audio interface (like an old RME or MOTU card) that will work with Logic 5.3.
If you cannot find a working "Emagic Logic Audio Platinum 5.3 download" or a dongle, do not despair. You can capture the vibe today: