41. The graphs of two inverse proportion functions $y=\frac{k_{1}}{x}$ and $y=\frac{k_{2}}{x}\left(k_{1}>k_{2}>0\right)$ in the first quadrant are shown in the figure. A moving point $P$ is on the graph of $y=\frac{k_{1}}{x}$, $P C \perp x$-axis at point $C$, intersecting the graph of $y=\frac{k_{2}}{x}$ at point $A, P D \perp y$-axis at point $D$, intersecting the graph of $y=\frac{k_{2}}{x}$ at point $B$.
(1) When $\frac{P A}{P C}=\frac{2}{3}$, $\frac{D B}{B P}=$ $\qquad$ ;
(2) If the coordinates of point $P$ are $(5,2)$, and the difference in the areas of $\triangle O A B$ and $\triangle A B P$ is $S$. Then when $k_{2}=$ $\qquad$, $S$ has the maximum value $\qquad$
Answer: (1) $\frac{1}{2}$; (2) $5, \frac{5}{2}$