Answer
$b=-5$ and $c=-7$
Work Step by Step
If $ax^{2}+bx+c=0$ and $5x^{2}-5x-7=0$, then $a=5$, $b=-5$, and $c=-7$.
In the quadratic equation all the coefficients and constant term are positive. Thus the problem $5x^{2}-5x-7=0$, would look like $5x^{2}+(-5x)+(-7)=0$, This will give you negative values for b and c.