5. Given $a>0, b>0$. Find the area of the triangle with side lengths $\sqrt{a^{2}+b^{2}}$, $\sqrt{a^{2}+4 b^{2}}$, and $\sqrt{4 a^{2}+b^{2}}$.
(Suppose $b>a$. Construct a rectangle with length $2b$ and width $2a$. $\sqrt{a^{2}+b^{2}}$, $\sqrt{a^{2}+4b^{2}}$, and $\sqrt{4a^{2}+b^{2}}$ can be regarded as the diagonal lengths of rectangles with sides $b$ and $a$, $2b$ and $a$, $b$ and $2a$, respectively. The required area is $\frac{3}{2}ab$.)