To me, the salient features of old-school play are (1) randomly generated and mechanically simple characters; (2) an open world or sandbox, and an XP system that encourages exploring it (preferably something concrete and diegetic, like XP = GP); (3) a campaign structure where enough time passes between active game sessions that real time can roughly keep pace with game time; (4) a need for characters to spend substantial downtime between adventures (because of healing, training, research, or tending to an estate or dominion), so as to intentionally create "gaps" where some characters are unavailable for adventuring during some sessions; (5) the understanding that said gaps are to be filled with newly-created 1st level characters, such that each player will eventually have a "stable" of PCs (of different levels) to choose from; and, perhaps most important of all, (6) that each adventure be player-driven rather than plot-driven (In that it's always the players who decide what their characters are going to do at the beginning of each adventure when they strike out from their home base).
5e is a poor match for the first point; could be made to fit the second, third, fourth, and sixth with a bit of tweaking; but generally doesn't admit to the possibility of point five — because everything about 5e and its attendant play-culture is centered on the concept of players playing their singular OC.