Does Modern Warfare support split-screen/co-op modes on PS5?

Solution 1:

The only Call of Duty available for the PS5 is Black Ops: Cold War (with Vanguard coming out later this year, on November 5). I'm going to assume that's not what you meant.

For the 2019 version of Modern Warfare, available on PS4:

According to GameRevolution, you can only do split-screen in the Spec Ops mode:

Split-screen co-op is currently only available in select multiplayer modes, specifically Spec Ops. Split-screen play is not available for the main campaign.

This is further confirmed by the game's official wiki, stating "[Special Ops] missions can be played solo, split screen, or online".

As you're well aware already, the original three Modern Warfare games all support split-screen co-op in their main campaigns. This is backed up by the wiki page for Split Screen:

Split screen allows multiple players to play on one screen. It divides part of the screen for each player. Split screen is featured in [...] Call of Duty 4: Modern Warfare, Call of Duty: World at War, Call of Duty: Modern Warfare 2, Call of Duty: Black Ops, Call of Duty: Modern Warfare 3, [list continues]

If you want to play split-screen co-op call of duty, you might need to go back to Black Ops 3, which does support it.