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I’m looking for clarification regarding combat space in a one-on-one combat situation, since it impacts disadvantage rolls and opportunity attacks.

If a medium size opponent attacks you with a melee weapon (one that does not increase reach), it’s assumed they are within 5′ of you (PHB 146). Based on the “SPACE” section in PHB 191-2, they are in one of 8 squares bordering yours. Regardless of whether it’s a hit or miss, it’s now your turn.

You’re a spell caster that only has an option of a ranged spell. Let’s assume you have no ‘touch’ spells and no melee weapon. Based on PHB 195, would you have disadvantage on your ranged spell attack roll because you’re within 5′? Or because each creature is in its own 5′ space, there is really 10′ between them combined, so there would be no disadvantage roll on the ranged spell attack?

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5' away

The PHB defines Space as (PHB, 191):

A creature's space is the area in feet that it effectively controls in combat, not an expression of physical dimensions...A creature's space also reflects the area it needs to fight effectively.

The variant rule for playing on a grid (PHB, 192) states:

To determine the range on a grid between two things - whether creatures or objects - start counting square from a square adjacent to one of them and stop counting in the space of the other one.

If Character A takes up 5' (one grid square) and Character B takes up 5' (one grid Square) and they are adjacent to each other, the distance between the two is 5'.

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    \$\begingroup\$ Another way to think of it is each character is in the center of the 5' space, placing them 2½' from the edge and 5' from each other. \$\endgroup\$ – sirjonsnow May 12 '17 at 12:27
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Range is commutative

In the beginning of your question you've already stated that the distance was 5′:

If a medium size opponent attacks you with a melee weapon (one that does not increase reach), it’s assumed they are within 5′ of you

it’s now your turn

If they ended their turn being 5′ of you, this naturally means that now you are within 5′ of them. Range is commutative, there can not be such situation when there are 5′ between A and B, but 10′ between B and A.

In comparison with the NautArch answer, this conclusion works with or without grid.

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