This is a great supposition based from today's standards. The fact is, there was no such thing as a "grid" or a "battlemat"...There were hexes. I remember those...and the graph paper we were encouraged to map on...but I am [fairly close to 100%] sure no one, no creature, no spell effect, traps, no thing was thought of in terms of a 5' square. Nada. My understanding is that was something brought in by 4e [could be wrong, maybe it was 3e, I don't actually know]. But in BECM or 1e terms, 5' square wasn't part of the game. Wasn't part of the consciousness playing the game.
OD&D certainly didn't have 5' squares - they came in as a requirement with 3.5 IIRC (or maybe 3E), but they had kinda been around for a while before that in the "Dungeon Floor Plans" that started with AD&D, I think. OD&D
did have 10' squares, though, on the maps - each 1/4" square on the map was generally considered to be 10 feet (or 1" in the "dungeon ground scale").
OD&D up to 3.x was certainly not expected mandatorily to be run using miniatures and a grid, but some sort of map and markers - whether miniature figurines or simply chits - have been used in most D&D games that I remember, starting with a cave with a dragon in and a huge "adventuring" party of mixed level characters fighting it on a map on a classroom desk somewhere around 1975/76 (i.e. my first ever encounter with D&D in any shape or form).
My first experience of routinely running without miniatures or markers at all came with (I think) Traveller in 1979 or 1980. After that it became increasingly common - games of Daredevils and Call of Cthulhu spring to mind, mostly because no suitable figures were (yet) available, I think.
The manner of using the figures changed, though, it has to be said. Early on, they were really used as an expression of what your character looked like, and they were used to show approximate spatial relationships - no precise grid or movement phasing system being in use. I found this to work OK, but it occasionally caused frustration and intense, blazing rows because one person's interpretation of whether a specific move was feasible or not differed drastically from another person's. With no movement phasing, whether you could move to cut off the orc from getting to the Magic User was a matter of opinion - and, if the DM didn't share yours you were SOL. I remember once being told my archer character couldn't target an enemy because he couldn't get his left (bow) arm around a wall without falling off the walkway he was stood on; I pointed out that the character was left-handed (because we had rules for that back then) and was told "well, you're left handed but taught to shoot a bow the "normal" way... Remind me what those handedness rules were for, again??