Yes. The game system for a game style does not matter. It's only a thing for people obsessed with the rule playing: some people like the game play where they encounter "mystery seven" and then roll a check and discover a clue.
5E works just fine for mysteries, as long as they are slightly above "Scooby Do" level mysteries. Magic and spells have all sorts of limits. And only the dumb npc do things in easy view of people and leave obvious clues. Even simple things like killing an npc from behind...then they don't know who killed them. And D&D is full of disguises and illusions and such. So, sure, talk to a dead body and he will say "the king of Orlor killed me"...and sure that is what they "remember seeing". And the sneaky killer could also cast 'speak with the dead' first....and then the 'good guys' can't cast it on the body when they find it...as per the spell description.
Though really, the Old School type play style goes around and over and beyond the rules. You can have a ton of spells, but you need to know how, when and where to use them. And 'core 5E really does not have investigation or detective type spells....
I add mystery to most adventures....and love players that solve mysteries For Real...not just rollout some dice to "solve" things. Though such players are rare.
