Answer
$$\frac{2}{3},\space\frac{4}{5},\space\frac{8}{7},\space\frac{16}{9},\space\frac{32}{11}$$
Work Step by Step
$$a_1=\frac{2^1}{2(1)+1}=\frac{2}{2+1}=\frac{2}{3}\\a_2=\frac{2^2}{2(2)+1}=\frac{4}{4+1}=\frac{4}{5}\\a_3=\frac{2^3}{2(3)+1}=\frac{8}{6+1}=\frac{8}{7}\\a_4=\frac{2^4}{2(4)+1}=\frac{16}{8+1}=\frac{16}{9}\\a_5=\frac{2^5}{2(5)+1}=\frac{32}{10+1}=\frac{32}{11}$$
