Answer
$1,-\frac{1}{4},\frac{1}{9},-\frac{1}{16},\frac{1}{25}$
Work Step by Step
$a_{n}=\frac{(-1)^{n-1}}{n^{2}}$
Substitute $1,2,3,4,5$ to $n$:
$a_{1}=\frac{(-1)^{1-1}}{1^{2}}=1$
$a_{2}=\frac{(-1)^{2-1}}{2^{2}}=-\frac{1}{4}$
$a_{3}=\frac{(-1)^{3-1}}{3^{2}}=\frac{1}{9}$
$a_{4}=\frac{(-1)^{4-1}}{4^{2}}=-\frac{1}{16}$
$a_{5}=\frac{(-1)^{5-1}}{5^{2}}=\frac{1}{25}$