The trick here is to notice that:
1] This is actually a disguised Geometric Progression from the 3rd term onwards: 2, 3, 5, 10, 20, 40, 80...
2] Because the Geometric Progression starts from the 3rd term of the set, the nth term in the set is actually the (n-2)th term of the Geometric Progression part of the set
Now armed with these two observation, apply the formula for nth term of any Geometric Progression = b X r^(n-1); remember b is 5 and n will be the 18th and 22nd term respectively, NOT 20th and 24th because of the 2nd observation above.
h = 18th term of the GP = 5 X 2^17
k = 22nd term of the GP = 5 X 2^21
k/h = 2^4 = 16
Therefore D is the correct answer.
Hope this helped.
The only ability the GMAT is an indicator of...is the ability to do well on the GMAT.