Answer
The vector field is not conservative.
Work Step by Step
1.First, in standard notation, these are the equations
$M-15y^3$, $N=-5xy^2$
2.In order to find out if the vector field is conservative, we see if they are equal. We take the derivative.
$\frac{dM}{dy}=45y^2, \frac{dn}{dx}=-5y^2 $
3. We finally say that they are indeed not equal, so the vector field is not conservative.
