For 9.17 you can use Vieta's formulas to find the sum of the roots. For a polynomial $P(x) = a_{n}x^{n}+a_{n-1}x^{n-1}+\cdots+a_{1}x+a_0$, the sum of all roots (real and complex, with multiplicities) is equal to $-\dfrac{a_{n-1}}{a_{n}}$.

For 9.18, let $x_1, \dots, x_5$ be the five roots. Since they are all solutions to the equation, we have their fifth powers can be written as $x_{i}^5 = -2x_{i} +1$ for $i = 1, \dots, 5$. You can use this to write a simpler expression for the sum of the fifth powers. You might need to use Vieta's formulas to finish.