\(\left(\dfrac{1}{2}\right)^{n+1}\cdot\left(\dfrac{1}{2}\right)^3=\left(\dfrac{1}{8}\right)^5\)
\(\Rightarrow\left(\dfrac{1}{2}\right)^{n+1}\cdot\left(\dfrac{1}{2}\right)^3=\left[\left(\dfrac{1}{2}\right)^3\right]^5\)
\(\Rightarrow\left(\dfrac{1}{2}\right)^{n+1+3}=\left(\dfrac{1}{2}\right)^{15}\)
\(\Rightarrow n+1+3=15\)
\(\Rightarrow n+4=15\)
\(\Rightarrow n=15-4\)
\(\Rightarrow n=11\)
