We can do this by substituting the values of $n$ from 1 to 5 into the given formula $a_{n}=(-1)^{n} 2^{n}$.
For $n=1$, $a_{1}=(-1)^{1} 2^{1}=-2$.
For $n=2$, $a_{2}=(-1)^{2} 2^{2}=4$.
For $n=3$, $a_{3}=(-1)^{3} 2^{3}=-8$.
For $n=4$, $a_{4}=(-1)^{4}
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