Does a large creature need to squeeze to fit into at 5' tall passageway?
From page 200 of the Essentials Rules Compendium:
Space: A creature's space is the area, measured in squares, that the creature occupies on the battle grid. This area represents the three-dimensional space that the creature needs to take part in an encounter, allowing it to turn around, attack, fall prone, and so on. Despite the cubic shape of its space, a creature is not actually a cube (unless it's a gelatinous cube).
So, to answer your question in short: Yes.
Large creatures require two squares in all dimensions for normal combat. Therefore, to fit into an area that is only one square high, they would need to squeeze.
I assume that they are filling cubic space for the most part. A longer creature might not be as tall as the creature is long.
If the tunnel was wide enough, though it seems like the monster could crawl.
I would rule that large creatures usually occupy cubic space. Not only does it make more sense it also makes tactical combat more interesting in situations where height matters.
I know that in previous editions, and specifically 3 and 3.5, that they did occupy cube space. And I believe that they specifically call that out in the PhB. Being at work right now, I am unable to look it up however.
I have always ruled that they do occupy cubic space, personally. Since Giants at 5 feet tall would be ... silly. :)
When you look at most creatures, the really large ones are usually big in area (3 squares or more) but not tall mathematically. Gravity has a funny affect on tall things, they tend to be unstable.
I apply the same logic to my game Creatures. Creatures up to medium in size can fit under a 5' height easily. No squeeze based on height. For each size category over medium I assume 2.5' of height on top of 5' for a creature when they are in a standing, relaxed, posture position.
So a 4sq x 4sq creature would be 5' + 10' high, 15' high. This seems to fit most creatures almost to a tee. Sometimes I have to over ride this rule, but in general it works really well.
So i would rule that a large creature would have to squeeze, unless their description lead me to think there were short.