To find the ratio of the areas of two squares given the ratio of their diagonals, follow these steps:

1. Diagonal of a Square Formula:
- For a square with side length \( s \), the length of the diagonal \( d \) is given by:
\[
d = s \sqrt{2}
\]

2. Ratio of Diagonals:
- Let the side lengths of the two squares be \( s_1 \) and \( s_2 \), and their diagonals be \( d_1 \) and \( d_2 \) respectively.
- Given that the ratio of the diagonals is \( \frac{d_1}{d_2} = \frac{2}{5} \), we have:
\[
\frac{s_1 \sqrt{2}}{s_2 \sqrt{2}} = \frac{2}{5}
\]
- This simplifies to:
\[
\frac{s_1}{s_2} = \frac{2}{5}
\]

3. Ratio of Areas:
- The area of a square is \( s^2 \), so the ratio of the areas \( A_1 \) and \( A_2 \) is:
\[
\frac{A_1}{A_2} = \left(\frac{s_1}{s_2}\right)^2
\]
- Substituting the ratio of the side lengths:
\[
\frac{A_1}{A_2} = \left(\frac{2}{5}\right)^2 = \frac{4}{25}
\]


The ratio of the areas of the two squares is 4:25.

The correct answer is C. 4:25.