5. (1990 American High School Mathematics Examination) First, select $a$ from $\{1,2,3, \cdots, 99,100\}$, then select $b$ from the same set. The probability that the last digit of $3^{a}+7^{b}$ is 8 is ( ).
A. $\frac{1}{16}$
B. $\frac{1}{8}$
C. $\frac{3}{16}$
D. $\frac{1}{5}$
E. $\frac{1}{4}$