Answer
See below.
Work Step by Step
$a_1=(-1)^1\frac{1+3}{1+2}=-\frac{4}{3}$.
$a_2=(-1)^2\frac{2+3}{2+2}=\frac{5}{4}$.
$a_3=(-1)^3\frac{3+3}{3+2}=-\frac{6}{5}$.
$a_4=(-1)^4\frac{4+3}{4+2}=\frac{7}{6}$.
$a_5=(-1)^5\frac{5+3}{5+2}=-\frac{8}{7}$.