To find the value of \( n \) that makes the ratios \(\frac{5}{4}\) and \(\frac{3}{0n}\) equivalent, we can set the two fractions equal to each other:
\[ \frac{5}{4} = \frac{3}{0n} \]
Cross-multiplying gives:
\[ 5 \cdot (0n) = 3 \cdot 4 \]
This simplifies to:
\[ 0 = 12 \]
This result is impossible, which means that there is no value of \( n \) that can make the ratios equivalent. In fact, since \( 0n \) will always equal 0 for any \( n \), the ratio \(\frac{3}{0n}\) is undefined whenever \( n \neq 0\).
Thus, there is no valid value for \( n \) that will satisfy the equation.