5. Several years ago, the age of the grandfather, who is over seventy, was 10 times the age of the grandson. Several years later, it will be 8 times the age of the grandson. If both the grandfather and the grandson are celebrating their birthdays today, then their ages are ( ) years.
(A) $71 、 8$
(B) $72 、 9$
(C) 73,9
(D) 74,10
5. A.

Let the current ages of the grandfather and grandson be $x$ years and $y$ years, respectively. The grandfather's age was 10 times the grandson's age $a$ years ago, and will be 8 times the grandson's age $b$ years from now. From the problem, we have:
$$
\left\{\begin{array}{l}
x-a=10(y-a), \\
x+b=8(y+b) .
\end{array}\right.
$$

Solving these equations, we get $x=36a+35b, y=\frac{9a+7b}{2}$.
Given $70<x<80 \Rightarrow 70<36a+35b<80$.
Since $a$ and $b$ are natural numbers, $a$ can only be 1, and $b$ is also 1.
Thus, $x=71, y=8$.