Answer
$-n+4$
Work Step by Step
Remember that:
$\sum_{k=1}^{n} 1=n$
and $\sum_{k=1}^{n} k=\frac{(1+n)n}{2}$
We find:
$\sum_{k=1}^{n}\left(-\frac{2 k}{n}+\frac{5}{n}\right)=-\frac{2}{n} \sum_{k=1}^{n} k+\frac{5}{n} \sum_{k=1}^{n} 1=\frac{5}{n} \cdot n-\frac{2}{n} \cdot \frac{(1+n)n}{2}=-(1+n)+5=5-n-1=-n+4$