Answer : Option D

Explanation :

$MF#%\dfrac{1}{(\sqrt{9}-\sqrt{8})} = \dfrac{(\sqrt{9}+\sqrt{8})}{(\sqrt{9}-\sqrt{8})(\sqrt{9}+\sqrt{8})}=\dfrac{(\sqrt{9}+\sqrt{8})}{9-8}= \sqrt{9}+\sqrt{8}\\\\$MF#%

$MF#%\text{Similarly all other terms can be rewritten. Thus,}\\\\
\dfrac{1}{(\sqrt{9}-\sqrt{8})}-\dfrac{1}{(\sqrt{8}-\sqrt{7})}+\dfrac{1}{(\sqrt{7}-\sqrt{6})}-\dfrac{1}{(\sqrt{6}-\sqrt{5})}+\dfrac{1}{(\sqrt{5}-\sqrt{4})}\\\\
= (\sqrt{9}+\sqrt{8}) - (\sqrt{8}+\sqrt{7}) + (\sqrt{7}+\sqrt{6}) - (\sqrt{6}+\sqrt{5}) + (\sqrt{5}+\sqrt{4})\\\\
=\sqrt{9}+\sqrt{4} = 3 + 2 = 5$MF#%