To solve the quadratic equation 5x^2 + 8x - 5008000 = 0, we can use the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / 2a

In this equation, a = 5, b = 8, and c = -5008000. Plugging these values into the quadratic formula, we get:

x = (-8 ± √(8^2 - 4(5)(-5008000))) / 2(5)
x = (-8 ± √(64 + 100320000)) / 10
x = (-8 ± √100320064) / 10
x = (-8 ± 10016) / 10

This gives us two possible solutions:

x = (-8 + 10016) / 10
x = 10008 / 10
x = 1000.8

and

x = (-8 - 10016) / 10
x = -10024 / 10
x = -1002.4

Therefore, the solutions to the quadratic equation 5x^2 + 8x - 5008000 = 0 are x = 1000.8 and x = -1002.4.