Stanza 5 Summary

Get out the microscope, because we’re going through this poem line-by-line.

Out of some subway scuttle, cell or loft
A bedlamite speeds to thy parapets,

Now the speaker abruptly moves away from the bridge again.
He talks about a deranged person ("bedlamite") who comes from the subway and lives in some dirty little room or apartment in the city.
"Bedlam" is a generic name for a mental asylum. The real Bedlam was an asylum in London.
The bedlamite "scuttles" out of the subway like a crab – a pathetic image.
A scuttle is also a bucket for holding coal, and the subway is a dirty place that looks as if it were smeared with coal.
If you've ever tried finding an apartment in New York City, you know what the speaker means by "cell"!
The bedlamite runs ("speeds") to one of the towers ("parapets") that holds up the suspension cables.
"Parapets" are found on castles, so the speaker is implicitly comparing the bridge to a castle.
The bedlamite is standing at the top of the bridge.

Tilting there momently, shrill shirt ballooning,
A jest falls from the speechless caravan.

Oh no! What's he doing up there? The insane guy went up to the bridge to commit suicide.
He stands "tilting" at the edge of the bridge's tower, gathering the courage to jump.
His shirt "balloons" in the wind up there. The shirt is "shrill," or loud (this is not a literal image).
And then… he "falls" off the bridge.
We never learn the name or anything else about this poor suicide, he's just another anonymous soul in the big city.
He is described as a "jest," like a jester or joker, or maybe just a joke.
Jesters often traveled in royal "caravans" in medieval times. (Ever been to a Renaissance Fair?)
In this case, the "caravan" might refer to the traffic on the bridge, or the bridge itself, which looks like it carries a procession of souls.
This is not a social caravan, it's an anonymous and impersonal, "speechless."