Answer
$$\displaystyle s_1=0 \\ s_2=\frac{3}{10} \\ s_3=\frac{8}{11} \\ s_4=\frac{5}{4} \\ s_5=\frac{24}{13}$$
Work Step by Step
We are given that $\{s_n\}=\dfrac{n^2-1}{n+8}$. In order to determine the first five terms, we will have to substitute $n=1,2,3,4,5$ into the given sequence:
$$\displaystyle s_1=\frac{1^2-1}{1+8}=\frac{0}{9}=0 \\ s_2=\frac{2^2-1}{2+8}=\frac{3}{10} \\ s_3=\frac{3^2-1}{3+8}=\frac{8}{11} \\ s_4=\frac{4^2-1}{4+8}=\frac{15}{12}=\frac{5}{4} \\ s_5=\frac{5^2-1}{5+8}=\frac{24}{13}$$
