For this exercise it is important to know that a "Conjugate" is.
By definition, a Conjugate is a binomial whose second term has sign that is opposite of the second term of the other binomial. For example, for:
[tex]a+b[/tex]Its conjugate is the following:
[tex]a-b[/tex]In this case you have the following expression:
[tex]5-\sqrt[]{x+4}[/tex]Then, applying the explained above, you get that its conjugate is:
[tex]5+\sqrt[]{x+4}[/tex]The answer is: Option D.