Define the generating functions $\text{B}(x)=\displaystyle{} \sum_{n=0}^{\infty} 2^{n} x^{n}$ and $F(x)=\displaystyle{} \sum_{n=0}^{\infty} f_{n} x^{n}$ where $f_{n}$ is the Fibonacci sequence determined by the recurrence relation
$$
\begin{aligned}
f_{0} &=0 \quad \text { and } \quad f_{1}=1 \\
f_{n} &=f_{n-1}+f_{n-2} & \text { for } n \geq 2\\
\end{aligned}
$$
Let $\text{G}(x)=\text{B}(x) \times \text{F}(x)$.
What is the coefficient of $x^{5}$ is $\mathrm{G}(x)?$
