To find the x-values of all points where the function has any relative extrema, we first need to find the derivative of the function f(x) = -x^2 - 5x - 1.
The derivative of f(x) is f'(x) = -2x - 5.
To find the x-values of the relative extrema, we set the derivative equal to 0 and solve for x:
-2x - 5 = 0
-2x = 5
x = -5/2
So, the x-value of the relative extrema is x = -5/2.
To find the value of the relative extrema, we substitute x = -5/2 into the original function f(x):
f(-5/2) = -(-5/2)^2 - 5(-5/2) - 1
= -25/4 + 25/2 - 1
= -25/4 + 50/4 - 4/4
= 21/4
Therefore, the value of the relative extrema is 21/4.