RPGaDay prompt 5 is “OLDEST game you’ve played”.
Oldest game overall
If we’re not talking about role-playing games, there’s Cluedo, Careers, Scrabble, Monopoly, or going back even further, chess, draughts (checkers), backgammon, cards. But the oldest game, apparently, is Mancala.

This could be played with simple pits scooped out of the sand plus stones, or more elaborate carved boards and pieces. Our board is made of wood and uses coloured glass beads.
There are two rows of six pits, plus two larger pits, one at each end. You start with three stones (or four according to official game rules) in each pit, plus the larger pits empty. Your pits are the six nearer you, and your store is the larger pit on your right.

- You take it in turns to choose a pit on your side, take all the stones from it and play them moving anti-clockwise, placing one stone in each pit you come to, plus your store if you reach it. Skip your opponent’s store.
- If you place the last piece in your own store, you get another turn.
- If you place the last piece in an empty pit on your side you capture that piece plus any pieces in the store opposite on your opponent’s side – placing in your store.
Once all pits on one side are empty, play ends, and the other player captures all the pieces remaining on their side, moving them to their store. The winner is the player with the most pieces in their store.
Oldest role-playing game

If we talk about role-playing games, since Dungeons and Dragons is really the only role-playing game I have played, it’s clearly the oldest. 1974, as the publication of the first ruleset by TSR, is probably the most appropriate starting date.
But of course it has had many editions (definitely more than the five that “fifth edition” would imply). I started playing with the Frank Mentzer Basic Set, but I did also play a couple of games of Advanced D&D.

Checking the dates on my manuals, I find the AD&D Monster Manual is 27 September 1977, the Players Handbook is 2 June 1978 and the Dungeon Masters Guide is 16 May 1979.
The Menzter Basic Set is February 1983, with publication in May, followed by the Expert Set in May 1983, publication July, Companion Set in April 1984 (no author date), Master Set Spring 1985, publication date June 1985, and Immortals Set June 1986 (again no author date).
So I suppose that makes my earliest role-playing game AD&D, but I played so little it feels more appropriate to say the BECMI boxed sets.
Oldest module

Well, I started with the classic “B2 Keep on the Borderlands”, which is copyright 1981, followed by X1 Isle of Dread, copyright 1981 and 1983. I also have B1-9 In Search of Adventure, which is a compilation published in 1987, which despite the name seems to be compiled from sections of modules B2 Keep on the Borderlands (actually just includes the Caves of Chaos) to B9 Castle Caldwell and Beyond (this contained five sections, and four of them form the first four parts of the compilation). So it doesn’t contain anything older than B2, and in actual fact the only module I’ve actually run from it was Castle Caldwell which is part of B9.
In terms of my own writing, I think this map is probably the earliest I have found other than my extensions to the castle in the Menzter Basic Set.