To solve the equation (x+1)^2 - 5x - 5 = 0, we can use the quadratic formula.

The quadratic formula states that for an equation of the form ax^2 + bx + c = 0, the solutions for x can be found using the formula:

x = (-b ± √(b^2 - 4ac)) / (2a)

In this case, a = 1, b = -5, and c = -5.

Plugging these values into the quadratic formula, we get:

x = (-(-5) ± √((-5)^2 - 4(1)(-5))) / (2(1))
x = (5 ± √(25 + 20)) / 2
x = (5 ± √45) / 2

Simplifying further, we have:

x = (5 ± √(9 * 5)) / 2
x = (5 ± 3√5) / 2

Therefore, the solutions to the equation (x+1)^2 - 5x - 5 = 0 are:

x = (5 + 3√5) / 2
x = (5 - 3√5) / 2