3. (5 points) This year, Lingling is 8 years old, and her grandmother is 60 years old. In \qquad years, her grandmother's age will be 5 times Lingling's age.
【Analysis】This problem can be solved by setting up an equation. Let $x$ be the number of years after which the grandmother's age will be 5 times Lingling's age. Then, in 5 years, Lingling's age will be $8+x$ years, and the grandmother's age will be $60+x$ years, which gives us the equation: $(8+x) \times 5=60+x$. Solving this equation will give us the answer.

【Solution】Solution: Let $x$ be the number of years after which the grandmother's age will be 5 times Lingling's age, then we have:
$$
\begin{array}{l}
(8+x) \times 5=60+x \\
40+5 x=60+x \\
4 x=20, \\
x=5 .
\end{array}
$$

Therefore, the answer is: 5.