For all values of $n$, the units digit of $\(3^{8 n+3}\)$ is 7 .

The units digit of $\(3^{8 n+3}+5\)$ is 2 and therefore, when $\(3^{8 n+3}+5\)$ is divided by 10 , it leaves a remainder 2 .

Therefore, Column $\(\mathrm{A}=2\)$. For all values of $n$, the units digit of $\(7^{8 n+3}\)$ is 3 . So, the units digit of $\(7^{8 n+3}+5\)$ is 8 and therefore, when it is divided by 10 , it leaves a remainder 8 .

Therefore, Column $\(\mathrm{B}=8\)$.

Hence, Column B $>$ Column A.

Thus, the correct answer is $B$.