When you have 5 instead of 4, what's the word instead of "quadrant"?

Solution 1:

Though a very rare word, that would be a quintant.

Solution 2:

Though "quintant" seems more correct to me for English Language, in practical English Usage the answer is, surprisingly, quadrant.

For example, the city of Portland, Oregon, US, is divided into five parts that they still call "quadrants:"

Folks in the city of Richmond, Virginia, USA also refers to five quadrants when discussing results of a poll by a small business association:

Extending beyond the map example OP asked about, a company called JDA also announces and reports itself as "the only company recognized as a leader in ALL FIVE Gartner Supply Chain Magic Quadrants!"

Finally, looking at Google Ngrams, "quintants" is not found in use (in Google's English corpus) even going back to 1800 while "five quadrants" is more common, not even counting instances where there are descriptive words between the two terms: