Can I get advantage against a monster when our characters are engaging it from two sides?

Question

Yesterday I played a game in a new group.

The Fighter (F) goes in and attacks the monster (M). Then it's my turn and I place my Rogue (R) opposite to the Fighter in regards to the monster. I was looking for the advantage in order to make a Sneak Attack, as I recall very vividly that such positioning gives advantage. So in the end our position looked like this:

+---+---+---+   F = Fighter
|   | F |   |   M = Monster
+---+---+---+   R = Rogue
|   | M |   |
+---+---+---+
|   | R |   |
+---+---+---+

My DM ruled that I didn't have advantage because such rule doesn't exist in D&D 5^th Edition. He however granted me my Sneak Attack because the Sneak Attack itself allows me to make such a hit in that situation.

I was a bit troubled because in every other group I played with, such a rule was accepted, and intensively used, even in groups without any Rogue. I checked the PHB and couldn't see any reference to this. So maybe such rule exist in the DMG?

So my question is: does such a rule for advantage exist? If yes, where is it defined? If not, does that idea of a rule come from any previous versions?

Answer 1

Flanking for advantage is an optional rule in DnD 5e

The flanking rule is given on Dungeon Master's Guide, page 251. It is an optional rule, and works as you describe. For squares:

When a creature and at least one of its allies are adjacent to an enemy and on opposite sides or corners of the enemy's space, they flank that enemy, and each of them has advantage on melee attack rolls against that enemy.

For hex grids:

When a creature and at least one of its allies are adjacent to an enemy and on opposite sides of the enemy's space, they flank that enemy, and each of them has advantage on melee attack rolls against that enemy.

However, since it is indeed an optional rule, it is up to your GM to decide whether the rule is in effect in your game or not. You can try to argue for or against, but they have the final call on the matter.

Answer 2

You don't have advantage, but you can make a sneak attack.

As @kviiri states in their answer, the "flanking grants advantage" rule in DMG pp 251 is optional. However, in the rogue's Sneak Attack class feature, we find the following text:

You don’t need advantage on the attack roll [to make a Sneak Attack] if another enemy of the target is within 5 feet of it, that enemy isn’t Incapacitated, and you don’t have disadvantage on the attack roll.

So your DM was correct that you can make a sneak attack, since the fighter is an enemy of the monster and is adjacent to it. Do note, however, that you'd still be able to make the sneak attack if the fighter was in the bottom-right square, since they'd still be adjacent to the monster.