First, we need to find the discriminant (D) of the quadratic equation:

D = b^2 - 4ac

In this case, the equation is in the form ax^2 + bx + c = 0, so:
a = -1
b = 5
c = 7

D = 5^2 - 4(-1)(7)
D = 25 + 28
D = 53

Now, we can find the roots of the quadratic equation using the quadratic formula:

x = (-b ± √D) / 2a

x1 = (5 + √53) / (2(-1))
x1 = (5 + √53) / -2

x2 = (5 - √53) / (2(-1))
x2 = (5 - √53) / -2

Therefore, x1 = (5 + √53) / -2 and x2 = (5 - √53) / -2.