1. **State the problem:** We have the polynomial function $$F(x) = 5x^5 + 6x^4 + cx^3 + dx - 5$$ and we know that $$x=1$$ is a root of this polynomial. 2. **Use the root condition:** If $$x=1$$ is a root, then $$F(1) = 0$$. 3. **Substitute $$x=1$$ into the polynomial:** $$F(1) = 5(1)^5 + 6(1)^4 + c(1)^3 + d(1) - 5 = 5 + 6 + c + d - 5$$ 4. **Simplify the expression:** $$5 + 6 + c + d - 5 = 6 + c + d$$ 5. **Set equal to zero and solve for $$c$$ and $$d$$:** $$6 + c + d = 0$$ 6. **Rewrite the equation:** $$c + d = -6$$ **Final answer:** The coefficients $$c$$ and $$d$$ satisfy the equation $$c + d = -6$$ if $$x=1$$ is a root of the polynomial.