a) To solve the equation (5+x)^3 = -27, we can take the cube root of both sides:

∛((5+x)^3) = ∛(-27)

5+x = -3

Now, subtract 5 from both sides:

x = -8

Therefore, the solution to the equation is x = -8.

b) To solve the equation (1-x)^2 = 1/9, we can take the square root of both sides:

√((1-x)^2) = √(1/9)

1-x = 1/3 or 1-x = -1/3

For the first case, subtract 1 from both sides:

-x = 1/3 - 1

-x = 1/3 - 3/3

-x = -2/3

Multiply both sides by -1 to solve for x:

x = 2/3

For the second case, subtract 1 from both sides:

-x = -1/3 - 1

-x = -1/3 - 3/3

-x = -4/3

Multiply both sides by -1 to solve for x:

x = 4/3

Therefore, the solutions to the equation are x = 2/3 and x = 4/3.

c) To solve the equation 5^3 + x = 125, we can subtract 5^3 from both sides:

x = 125 - 5^3

x = 125 - 125

x = 0

Therefore, the solution to the equation is x = 0.