To solve the equation cos(-5x) = -0.5, we can use the identity cos(-x) = cos(x) and the fact that cos(pi/3) = 0.5.

So, we have cos(-5x) = cos(5x) = -0.5.

From this, we can determine the value of x by finding the angle whose cosine is -0.5. The angle whose cosine is -0.5 is 2pi/3 or 120 degrees.

So, 5x = 2pi/3 + 2pi*k or 5x = 120 + 360k, where k is an integer.

Now, to solve the equation cot(-6x) = -1, we know that cot(x) = 1/tan(x). So, we have cot(-6x) = 1/tan(-6x) = -1.

This implies that tan(-6x) = -1.

The angle whose tangent is -1 is -pi/4 or -45 degrees.

So, -6x = -pi/4 + pi*k or -6x = -45 + 180k, where k is an integer.

Therefore, the solutions to the equations are x = (2pi/3 + 2pik)/5 and x = (-pi/4 + pik)/6.