Since triangles \( \Delta ABC \) and \( \Delta AXY \) are similar with a ratio of \( \frac{5}{3} \), we can set up a proportion based on the corresponding sides.
Given that \( BC = 25 \), this corresponds to side \( XY \) in triangle \( AXY \). The ratio of the lengths of the sides is given by:
\[ \frac{AB}{AX} = \frac{BC}{XY} = \frac{5}{3} \]
To find \( XY \), we can use the following equation derived from the ratio:
\[ \frac{25}{XY} = \frac{5}{3} \]
Cross-multiplying gives:
\[ 5 \cdot XY = 25 \cdot 3 \]
Calculating the right side:
\[ 5 \cdot XY = 75 \]
Now, divide both sides by 5 to solve for \( XY \):
\[ XY = \frac{75}{5} = 15 \]
Thus, the length of \( XY \) is \( \boxed{15} \).