Substituting the values in the formula
Combined SD $= \sqrt { \large\frac{20 \times 5^2+ 20 \times 5^2}{20+20}+\frac{20 \times 20 (17-22)^2}{(20+20)^2}}$
$\qquad= \sqrt {\large\frac{1000}{40}+\frac{400 \times 5^2}{40^2}}$
$\qquad= \sqrt {\large\frac{1000}{40} +\frac{400 \times 5^2}{40^2}}$
$\qquad= \sqrt {\large\frac{1000}{40} +\large\frac{10000}{40 \times 40}}$
$\qquad= \large\frac{1}{40} $$ \sqrt { 40000+10000}$
$\qquad= \large\frac{1}{40}$$ \sqrt {50000}$
$\qquad= \large\frac{223.606}{40}$
$\qquad= 5.59$
$\therefore $ The combined standard deviation of the set obtained are $5.59$
Hence B is the correct answer.