Answer: 3 more.

Solution: The arithmetic mean of the numbers $\frac{a+b}{2}, \frac{b+c}{2}, \frac{a+c}{2}$, obviously, coincides with the arithmetic mean of the numbers $a, b, c$. Therefore, if one $\frac{a+b}{2}$ is 5 more, and $\frac{a+c}{2}$ is 8 less, then, to get the same result, $\frac{b+c}{2}$ must be 3 more.
7. Given three numbers $a, b, c$. It is known that the arithmetic mean of the numbers $a$ and $b$ is 5 more than the arithmetic mean of all three numbers. And the arithmetic mean of the numbers $a$ and $c$ is 8 less than the arithmetic mean of all three numbers. By how much does the arithmetic mean of the numbers $b$ and $c$ differ from the arithmetic mean of all three numbers?