Interception at $x-$axis is $\ln \ x=0.1$ and slope $=-0.02$
Equation fo straight line is given by,
$y=mx+C$
According to the question,
$y=m(\ln \ x)+C$ where $m=-0.02$
$y=-0.02(\ln \ x)+C\quad \rightarrow(1)$
Abscissa is known as intercept in $x-$axis i.e. for $y=0,\ln \ x =0.1$
From equation $(1),$
$0=-0.02\times 0.1+C$
$C=0.002\quad \rightarrow(2)$
From equations $(1)$ and $(2),$
$y=-0.02(\ln \ x)+0.002$
At $x=5,$
$y=-0.02(\ln \ 5)+0.002$
$y=-0.030$
So, the correct answer is $(A).$