5. Given a fixed point $A(1,1)$, and $F$ is the left focus of the ellipse $\frac{x^{2}}{8}+\frac{y^{2}}{4}=1$. A moving point $P$ is on the ellipse. Try to find the maximum and minimum values of $|P F|+|P A|$, and the coordinates of point $P$ when these values are achieved.
5. Let $F_{1}, F_{2}$ be the left and right foci, respectively. Since $\left|P F_{1}\right|+|P A|=\left(\left|P F_{1}\right|+\left|P F_{2}\right|\right)+\left(|P A|-\left|P F_{2}\right|\right)=4 \sqrt{2}+$ $\left(|P A|-\left|P F_{2}\right|\right)$, it is easy to see that $-\left|A F_{2}\right| \leqslant|P A|-\left|P F_{2}\right| \leqslant\left|A F_{2}\right|$, with equality holding only when $P, A, F_{2}$ are collinear. Therefore, the maximum value of $\left|P F_{1}\right|+|P A|$ is $2 a+\left|A F_{1}\right|=5 \sqrt{2}$, and the minimum value is $2 a-\left|A F_{2}\right|=3 \sqrt{2}$.