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All the variants of the payload fairing for Ariane 5 are 5.4 meters in diameter, the same as the core stage of the rocket. At the same time, the mirror of the James Webb Space Telescope is 6.5 meters. That looks like a very basic geometric problem to me. Although the mirror is modular, it is supposed to be launched in one piece, and not assembled in orbit.

There is even a diagram of the telescope nicely fitting in the fairing:

JWST in payload fairing

By NASA (James Webb Space Telescope in Ariane 5 fairing) [Public domain], via Wikimedia Commons

The only possibility I can see is that the payload fairing is custom made significantly wider than any earlier fairing.

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The JWST is made to fold up, to fit inside the standard fairing. You can sort of see this in your image, 3 mirror segments are visible (the hexagons in the middle), other segments are viewed side-on and aren't visible.

Folding animation

Time lapse showing the folding during assembly

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    $\begingroup$ By the time we can get people into space easily, we won't actually need people in space. Robotics and AI will handle everything - except of course to fill the rooms and zero-gee swimming pools of the space-hotels, and of course as a "backup bio population" if Earth is destroyed and the AI still needs us or at least wants to keep us around. The JWST is an amazing thing - self-assemble, self-align, self-operate, self-correct its unstable orbit... Therefore this question. $\endgroup$
    – uhoh
    Commented Oct 5, 2016 at 11:18

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