Answer: \(x=3\), \(y=\frac{9}{2}\).

Use substitution to reduce the simultaneous equations to one equation in one unknown, then substitute back to find the other unknown.

From \(\frac{y}{x}=\frac32\), we have \(y=\frac32x\).

Substitute this into \(\frac{y^4}{x^5}=\frac{27}{16}\):

\(\frac{\left(\frac32x\right)^4}{x^5}=\frac{27}{16}\).

So \(\frac{81}{16x}=\frac{27}{16}\), giving \(x=3\).

Then \(y=\frac32(3)=\frac92\).

This gives the required answer: \(x=3\), \(y=\frac{9}{2}\).