MMORPGs like World of Warcraft or Guild Wars 2 are a great way to play together. With 5 players you can exactly fill a party in both games.

RTS games like Starcraft 2 (which is free now) or Age of Empires could also be fun, but 5 players is a bit awkward because it’s too many for a single team and uneven so you can’t play like a 3v3. But at least in SC2 there’s a 2v2 and a 3v3 ladder so you could always split into two teams or play a free for all. There are also a bunch of cool custom games in the arcade like Ice Baneling Escape or Zealot Hockey you could try.

Very different, but Trackmania is also fun with friends. Not the right choice if you enjoy ramming your friends off the road, but there are probably other games for that too. To set up and play in a club/server you’d need club access which costs like $20 a year, but you can try the game for free first to see if you like it. You can compete for records on a map, play an RPG together (a map style where the focus is on finding the right way instead of just racing) or build tracks for each other.

You could try an ARPG, unfortunately most of them (Diablo, Grim Dawn, Last Epoch) seem to limit parties to 4 players, but Path of Exile allows up to six. And if you’re not serious about the end game you’ll never need to spend any money (if you are it’s like $40 for stash tabs one time and you’re set forever).