What are some tips for passing qualifying written exam (i.e., writing a lot in a week)?
Step one, plan your writing. The most efficient way to work is to write an outline before you start.  However, in this case, where you have five days, you might need to alternate activities -- researching, trying out ideas, outlining and writing up parts you feel pretty sure about.  So you might find that after a couple of days of this, you've written a large part of your submission, without having gone strictly step by step (outline, then write from the outline).  In this case, you may have to produce an outline from your written paragraphs.  You might need to do this more than once.  Definitely do work with an outline, though, even if it's a bit of a pain to analyze your existing paragraphs and then describe them with an outline.

Why?  Because this will help you find places where you're being repetitive, or where you make a leap of faith and omit to explain how you got from Point A to Point B, or where some reordering would make things hang together better.

If you need to consider a major restructuring, it can help to print it all out and cut it up into pieces according to sub-topic, and then try laying out the pieces in a few different orders on the floor or a large table.

Ideally, though, after having written an outline, you would then churn out reams of words and sentences and paragraphs, using your outline as your guide. 

Revision: Let some time go by -- half a day, or overnight, before proceeding to the revision stage. Ideas for finding errors and places that aren't clear: Read it out loud. Display it in a different font or different size, or on a different screen. Print a hard copy. Have the computer read it to you out loud.  These things will make it easier for you to find problems.

If you're allowed to, ask a friend to read a draft and circle anything that seems unclear or possibly having a spelling, punctuation or grammar mistake.

(The best way of all to prepare for writing is to pre-write with an interested live human being, who asks you, "What is your essay going to be about?")

Get lots of exercise and sleep between now and then, of course.  Make sure you have a reliable set-up with all the resources and tools and groceries and peace and quiet you will need, including headphones or ear plugs if noise bothers you.  Alert friends and acquaintances that you will be on the dark side of the moon for five days.

Use version control.  Save a new, numbered version every couple of hours.  Make sure your computer does an autorecover save when it crashes.

Practice makes perfect, and this is especially true with writing -- and revising.  So, you may wish to warm up your writing and revising skills between now and then.

Remember that they won't be grading only on the quality of the writing, and that lots of students find writing challenging, but somehow many of them graduated.