To solve the equation \(\frac{16x}{5y} = \frac{5x}{y}\), follow these steps:

1. Start with the given equation:
\[
\frac{16x}{5y} = \frac{5x}{y}
\]

2. Cross-multiply to eliminate the fractions:
\[
16x \cdot y = 5x \cdot 5y
\]

3. Simplify the equation:
\[
16xy = 25xy
\]

4. Subtract \(16xy\) from both sides to isolate the terms involving \(xy\):
\[
16xy - 25xy = 0
\]

5. Combine like terms:
\[
-9xy = 0
\]

6. Divide both sides by \(-9\):
\[
xy = 0
\]

7. Since \(xy = 0\), either \(x = 0\) or \(y = 0\).

So, the solutions to the equation are \(x = 0\) or \(y = 0\).