1. **State the problem:** Find $\frac{d^5y}{dx^5}$ for the function $y=3x^4+2x^3-4x^2+x+5$.\n\n2. **Recall the formula:** The $n$th derivative of a polynomial term $ax^m$ is given by \n$$\frac{d^n}{dx^n}(ax^m) = a \cdot \frac{m!}{(m-n)!} x^{m-n}$$ if $m \ge n$, otherwise the derivative is 0.\n\n3. **Calculate derivatives term-by-term:**\n- For $3x^4$, the 5th derivative is 0 because $4 < 5$.\n- For $2x^3$, the 5th derivative is 0 because $3 < 5$.\n- For $-4x^2$, the 5th derivative is 0 because $2 < 5$.\n- For $x$, the 5th derivative is 0 because $1 < 5$.\n- For constant $5$, all derivatives are 0.\n\n4. **Conclusion:** Since all terms vanish by the 5th derivative,\n$$\frac{d^5y}{dx^5} = 0.$$