Export file settings to print at ultra-high-resolution: 5000 dpi, 1x1cm

I have a series of files each with a 1024x1024 artboard, with different patterns on each one.
I need to export them to be printed at ultra-high-resolution (5000 dpi, with a physical size of about 1cm x 1cm) to be used with a particular kind of new micro-optic technology.
How do I export the vector images to be rendered properly for printing at a specific dpi, and a specific size?

I understand the math better now, but am still stuck on how to set the size using File>Export.
When exporting as a JPEG file, for example, I have the following options:
If I enter 5000 ppi in the Resolution field (or even 2400), I get an error that Illustrator can't export at that high a resolution. I tried opening the Illustrator files directly in Photoshop, but the images are distorted and unusable as they appear there.
I don't see any options to set the image size to 2000x2000 pixels upon export. Sorry if I am being obtuse--I feel I must be missing something very basic here!

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    C:\Program Files (x86)\Adobe\Acrobat 11.0\Acrobat\plug_ins\Accessibility.api
        Версия: 11.0.9.29
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        Время создания: 13:44:20
    C:\Program Files (x86)\Adobe\Acrobat 11.0\Acrobat\plug_ins\Annots.api
        Версия: 11.0.9.29
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    C:\Program Files (x86)\Adobe\Acrobat 11.0\Acrobat\plug_ins\IA32.api
        Версия: 11.0.9.29
      Дата создания: 2014/09/12
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    C:\Program Files (x86)\Adobe\Acrobat 11.0\Acrobat\plug_ins\PaperCapture.api
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    C:\Program Files (x86)\Adobe\Acrobat 11.0\Acrobat\plug_ins\SaveAsRTF.api
        Версия: 11.0.9.29
      Дата создания: 2014/09/12
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    C:\Program Files (x86)\Adobe\Acrobat 11.0\Acrobat\plug_ins\SendMail.api
        Версия: 11.0.9.29
      Дата создания: 2014/09/12
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    C:\Program Files (x86)\Adobe\Acrobat 11.0\Acrobat\plug_ins\Updater.api
        Версия: 11.0.9.29
      Дата создания: 2014/09/12
        Время создания: 13:44:22

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