5. As shown in Figure 5, in a square $ABCD$ with a side length of 10, six identical smaller squares are inscribed, with vertices $P, Q, M, N$ of the smaller squares lying on the sides of the larger square. Then the sum of the areas of these six smaller squares is
5.32. 64 .

As shown in Figure 8, passing through
each vertex of the small squares
draw parallel lines to each side,
forming a "string diagram",
where the longer leg of the small right
triangle is $a$, and the shorter leg is $b$. Then
$$
\begin{array}{l}
\left\{\begin{array}{l}
2 a+5 b=10, \\
5 a=10
\end{array}\right. \\
\Rightarrow\left\{\begin{array}{l}
a=2, \\
b=1.2 .
\end{array}\right.
\end{array}
$$

Figure 8

Therefore, the area of a small square is
$$
2^{2}+1.2^{2}=5.44 \text {. }
$$

Thus, the area of six small squares is
$$
5.44 \times 6=32.64 \text {. }
$$