To receive grade 'A' in a course, one must obtain an average of 90 marks or more in five papers each of 100 marks.

Let x be the minimum marks scored in the last paper.

Then, $90 \leq \frac{87+95+92+94+x}{5} \leq 100$

$\Rightarrow 90 \leq \frac{368+x}{5} \leq 100$

$\Rightarrow 450 \leq 368+x \leq 500$

$\Rightarrow 450-368 \leq 368+x-368 \leq 500-368$

$\Rightarrow 82 \leq x \leq 132$

But $x$ can not be more than 100

$\Rightarrow 82 \leq x \leq 100$

Hence, the minimum marks that Shikha must score in the fifth paper is 82 .