Upgrade requires more money
UPDATE: Sony backflips on decision to charge PS4 users to upgrade, stating 'Players who purchase Horizon Forbidden West on PlayStation 4 will be able to upgrade to the PlayStation 5 version for free'.
As revealed in an FAQ regarding the various special editions of Horizon Forbidden West - Digital Deluxe Edition, Collector’s and Regalla Edition - are the only available options for a PlayStation 5 upgrade.
For owners of the Standard and Special Editions this is not the case, and players must purchase the more expensive versions to get the upgrade.
You can still play the PS4 version on PS5, though it will not feature any exclusive content from the new console.
There is so much content differentiation in the purchase options for Horizon Forbidden West, that Sony had make an FAQ.