As the average of 5 numbers $$x_1, x_2, x_3, x_4 \& x_5$$ is $$S$$, we get their sum as $$\mathrm{x}_1+\mathrm{x}_2+\mathrm{x}_3+\mathrm{x}_4+\mathrm{x}_5=5 \mathrm{~S)$$

Similarly as the average of 3 numbers $$y_1, y_2$ & $y_3$$ is $$R$$, we get their sum as

$$\(y_1+y_2+y_3=3 R\)$$


Finally the combined average of $$x_1, x_2, x_3, x_4, x_5$ & $\quad y_1, y_2, y_3$$ is $$\frac{\left(x_1+x_2+x_3+x_4+x_5\right)+\left(y_1+y_2+y_3\right)}{5+3}=\frac{5 S+3 R}{8}$$

Hence the answer is (A).