Answer
$\sum_{k=5}^{17}\left(-3^{k-1+3^{k}}\right)=3^{17}-3^{4}$
Work Step by Step
We find:
$\sum_{k=5}^{17}\left(3^{k}-3^{k-1}\right)=-3^{5}+3^{7}-3^{6}+3^{5}-3^{4}+3^{6}+\ldots+3^{17}-3^{16}$
$=-3^{8}+3^{7}-3^{8}+3^{8}-3^{4}+3^{8}+\ldots+3^{17}-3^{16}$
$=3^{17}-3^{4}$
