$$f\left(x\right)=\frac{1}{1+x}$$
$$f\left\{f\left(x\right)\right\}=\frac{1}{1+\frac{1}{1+x}}\ =\ \frac{\left(x+1\right)}{x+1+1}\ =\ \frac{x+1}{x+2}$$
$$f\left[f\left\{f\left(x\right)\right\}\right]=\frac{1}{1+\frac{x+1}{x+2}}\ =\ \frac{\left(x+2\right)}{x+2+x+1}\ =\ \frac{x+2}{2x+3}$$

at x=5;
$$f\left[f\left\{f\left(5\right)\right\}\right]=\ \frac{5+2}{2\left(5\right)+3}=\frac{7}{13}$$
Multiplying numerator and denominator by 3
$$\frac{7\cdot3}{13\cdot3}\ =\ \frac{21}{39}$$
Answer is B