CoraQuest is a fun kid-friendly cooperative dungeon crawl that my 6yo and I really enjoy. (Edit): Rereading, I forgot the part about your kid turning five, so this may be a bit advanced.
Outfoxed! (2014) has been mentioned several times and I also recommend it. It’s a cooperative, clue-esque deduction game.
I remember seeing an article or a video about people in prison using two disposable cups because they weren’t allowed dice. You write numbers on the outside near the rim of one cup when holding it upside down, and mark or cut the other in a way that identifies the number when nested on top of the numbered cup. You then spin the upper/outer cup to “roll”