Multiply. \[ \frac{5 y}{4 b^{2}} \cdot \frac{8 b^{3} y}{y^{5}} \]

Step 1 ：Given the two fractions \(\frac{5 y}{4 b^{2}}\) and \(\frac{8 b^{3} y}{y^{5}}\)

Step 2 ：When multiplying fractions, we multiply the numerators together to get the new numerator and the denominators together to get the new denominator.

Step 3 ：So, we multiply the numerators \(5y\) and \(8b^{3}y\) together and the denominators \(4b^{2}\) and \(y^{5}\) together.

Step 4 ：We also need to simplify the result if possible.

Step 5 ：After simplifying, we get the final result as \(\frac{10 b}{y^{3}}\)

Step 6 ：Final Answer: The result of the multiplication is \(\boxed{\frac{10 b}{y^{3}}}\)