Answer
See below.
Work Step by Step
Plugging in the respective values of $n$:
$a_1=(-1)^1\frac{5\cdot1}{2\cdot(1-1)+1}=-\frac{5}{1}=-5$
$a_2=(-1)^2\frac{5\cdot2}{2\cdot(2-1)+1}=\frac{10}{3}$
$a_3=(-1)^3\frac{5\cdot3}{2\cdot(3-1)+1}=-\frac{15}{5}=-3$
$a_4=(-1)^4\frac{5\cdot4}{2\cdot(4-1)+1}=\frac{20}{7}$
$a_5=(-1)^5\frac{5\cdot5}{2\cdot(5-1)+1}=-\frac{25}{9}$
