Answer
$$ n=5,\:n=-2,\:n=2$$
Work Step by Step
Solving the equation, we find:
$$ n^5-5n^4-16n+80=0 \\ \left(n-5\right)\left(n^2+4\right)\left(n+2\right)\left(n-2\right)=0 $$
Considering only the real solutions:
$$ n=5,\:n=-2,\:n=2$$
You can help us out by revising, improving and updating this answer.
Update this answerAfter you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.