What are the best cooperative board games for 4-5 players?

The best cooperative games for that player count are ones that scale well without becoming chaotic. Pandemic is the classic that works perfectly even at 5, the pace stays tense and everyone has a well-defined role. Then there's Arkham Horror: The Card Game if you like the investigative theme and aren't put off by some complexity. Spirit Island is more demanding but fantastic if you're willing to invest time in setup and rules; with 4-5 players the game really pushes cooperation to the max.

Another category that works is narrative games. Gloomhaven is heavy and long but offers a real campaign; Jaws of the Lion is a leaner version if you don't want to go season by season. If you prefer something faster, Forbidden Island is light but strategic enough, though some people find it too simple after a few plays.

It depends on how much time you have, how much rule complexity you prefer, and whether you care about theme. Pandemic remains the most universal: pretty much everyone knows how it works, there are no nasty mechanical surprises, and it works well at any number in your range.