1. **State the problem:** Solve the equation $$15y + 5y^3 + 3y^5 = 5x^3$$ for $y$ in terms of $x$. 2. **Rewrite the equation:** $$15y + 5y^3 + 3y^5 = 5x^3$$ 3. **Divide both sides by 5 to simplify:** $$\frac{15y}{5} + \frac{5y^3}{5} + \frac{3y^5}{5} = \frac{5x^3}{5}$$ 4. **Cancel common factors:** $$3y + y^3 + \frac{3}{5}y^5 = x^3$$ 5. **Rewrite the equation:** $$3y + y^3 + \frac{3}{5}y^5 - x^3 = 0$$ 6. **This is a nonlinear equation in $y$ involving powers up to 5.** 7. **No simple algebraic factorization is apparent, so $y$ is implicitly defined by:** $$3y + y^3 + \frac{3}{5}y^5 = x^3$$ 8. **For specific $x$ values, $y$ can be found numerically.** **Final answer:** The implicit solution is $$3y + y^3 + \frac{3}{5}y^5 = x^3$$