$G(x) = \sum_{n=0}^{\infty}2^nx^n \times \sum_{r=0}^{\infty}f_rx^r$

$= \sum_{n=0}^{\infty} \sum_{r=0}^{\infty}\ 2^nf_r \ x^{n+r}$

$n+r=5 \implies n=5-r,$ So,

$[x^5] \sum_{r=0}^{5}\ 2^{5-r}f_r $

Answer= $2^5.0+2^4.1+2^3.1+2^2.2+2^1.3+2^0.5 =43$

$= \sum_{n=0}^{\infty} \sum_{r=0}^{\infty}\ 2^nf_r \ x^{n+r}$

$n+r=5 \implies n=5-r,$ So,

$[x^5] \sum_{r=0}^{5}\ 2^{5-r}f_r $

Answer= $2^5.0+2^4.1+2^3.1+2^2.2+2^1.3+2^0.5 =43$