Activision has clarified in a post on social media that the PS5 & PS4 versions of Call of Duty: Black Ops and Call of Duty: Black Ops II support Cross-Play.
Both games launched for Sony’s current and last generation consoles late last week, although it was soon revealed they were somewhat barebones ports with no major visual upgrades or other features such as 120 FPS. However, at the time there was some confusion about whether or not they supported Cross-Play.
PS4 and PS5 players are able to matchmake with one another. There is no cross-platform play with PS3 or other hardware platforms. Also, Season Pass owners are able to matchmake with non-Season Pass owners in both titles.
Call of Duty: Black Ops and Call of Duty: Black Ops II are currently available for $19.99 each for a limited time, and will cost $39.99 from August 6 onwards. Both titles include the Campaign, Multiplayer, and Zombies content plus Trophy support. Black Ops originally launched in November 2010 for PS3, PC, DS, Wii, and Xbox 360 with Black Ops 2 following two years later on PS3, PC, Wii U, and Xbox 360.
[Source – Call of Duty Updates on X]