5. In a right triangle $A B C$, from the vertex of the right angle $C$, the bisector $C L,|C L|=a$, and the median $C M,|C M|=b$ are drawn. Find the area of triangle $A B C$.
5. Denoting the legs by $x$ and $y$, we obtain the system of equations

$$
\left\{\begin{aligned}
a & =\frac{x y \sqrt{2}}{x+y} \\
4 b^{2} & =x^{2}+y^{2}
\end{aligned}\right.
$$

from which we will find $x y$.

Answer: $\frac{a^{2}+a \sqrt{a^{2}+8 b^{2}}}{4}$.