From lens formula, we have
$\frac{1}{v}-\frac{1}{u}=\frac{1}{f}$
Here, $f=5 \,cm$.
Taking the least count (error) of the measuring scale to be
$1 \,mm =0.1 \,cm$, for the worst case,
we get $\frac{\Delta f}{f}=\frac{\Delta u}{u}+\frac{\Delta v}{v}+\frac{\Delta(u+v)}{u+v}$
(by using $f =\frac{u v}{u+v}$ )
Therefore,
$\frac{\Delta f}{f}=\frac{0.1}{10}+\frac{0.1}{10}+\frac{0.2}{2.0}=\frac{3}{100} $
$\Rightarrow \Delta f=\frac{3}{100} \times 5=\frac{3}{20}=0.15$
The closest answer is $f=5.00 \pm 0.10\, cm$, that is, option (D).
