For this one let's look carefully at how the word is spelled in each option:

The sentence refers to applying for some type of housing "on the campus" 

Of the options, only E "accommodation" is spelled correctly for this meaning of housing or lodging.

Choices A, B, C, D all have misspellings of the root word "accommodate".

Option E "accommodation" correctly matches the intended housing concept. 

Therefore, to best complete the sentence with the right spelling matching the intended housing context, choice E "accommodation" is the word that fits.