To solve the equation \( x^2 = \frac{25}{64} \), we start by taking the square root of both sides.
\[ x = \pm \sqrt{\frac{25}{64}} \]
Calculating the square root, we have:
\[ \sqrt{\frac{25}{64}} = \frac{\sqrt{25}}{\sqrt{64}} = \frac{5}{8} \]
Thus, the two solutions for \( x \) are:
\[ x = \frac{5}{8} \quad \text{and} \quad x = -\frac{5}{8} \]
Now, we need to present the solutions, starting with the lesser number:
\[ -\frac{5}{8}, \frac{5}{8} \]
So the final answer is:
\[ -\frac{5}{8}, \frac{5}{8} \]