Forza Horizon 5 was released on 9 November 2021 for Xbox One, Xbox Series X|S, and PC, with Premium Edition owners getting early access from 5 November 2021.

Since you seem interested in timing, one extra bit: the game later arrived on PlayStation 5, where Premium Edition owners could start playing on 25 April 2025, and the general release on PS5 was 29 April 2025.

Information gathered from public forums or data available on the internet and portrayed here.