The moon is about 30 arcminutes across (half a degree) [0], which is considerably larger than the area of the Extreme Deep Field. But the estimate of the number of galaxies is okay.
The Hubble Ultra-Deep Field (of which the Extreme Deep Field is a part) is one thirteen-millionth part of the full sky. [1]
The full sky is about 41,253 square degrees in size. [2]
I think the HXDF is one 32-millionth of the full sky. If so,
multiplying 32 million by the 5500 galaxies in the XDF gives on the order of 200 billion galaxies, as you said.
Yes, you're right, thanks for the correction: the Extreme Deep Field image is smaller than the moon. I neglected to click on the image at [1], thereby missing the detail in the full size image[2].
1. https://en.wikipedia.org/wiki/Hubble_eXtreme_Deep_Field 2. https://en.wikipedia.org/wiki/Hubble_eXtreme_Deep_Field#/med...