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:

Its conjugate is the following:

In this case you have the following expression:
![5-\sqrt[]{x+4}](https://img.qammunity.org/2023/formulas/mathematics/college/xsmxr3pnkwiyn0you765qp51gno2fmql7k.png)
Then, applying the explained above, you get that its conjugate is:
![5+\sqrt[]{x+4}](https://img.qammunity.org/2023/formulas/mathematics/college/ri2qpyhrr98i1jbmdcdtxvvxyoittji9ay.png)
The answer is: Option D.