8. Two people agree: to go to place $A$ together on a certain day, meeting at place $B$ between 7:00 AM and 8:00 AM. The one who arrives at $B$ first will wait for a maximum of $5 \mathrm{~min}$, and if the other does not show up, they will go ahead. Assume the times at which the two people arrive at $B$ are random, independent, and equally likely. Then, the probability that the two people will be able to go to $A$ together on that day is $\qquad$
8. $\frac{23}{144}$.

Let the times when the two people arrive at location $A$ be 7:00 plus $m$ minutes and 7:00 plus $n$ minutes $(0 \leqslant m, n \leqslant 60)$. Represent the times when the two people arrive at location $A$ with the pair $(m, n)$. In a Cartesian coordinate system, the domain of point $(m, n)$ is a square with a side length of 60, and its area is 3600.

Clearly, the two people can go to location $A$ together on the same day if and only if $|m-n| \leqslant 5$.
In this case, the domain of the corresponding points is the region between the two lines $m-n = \pm 5$ within the square (as shown in Figure 4), and its area is
$$
\begin{array}{l}
3600-55^{2} \\
=575 .
\end{array}
$$

Therefore, the required probability is $\frac{575}{3600}=\frac{23}{144}$.