To solve this system of equations, we can use the method of substitution or elimination.

Let's use the substitution method:

From the first equation, we can isolate y:

y = -24 - 4x

Now we substitute this expression for y in the second equation:

-x - 5(-24 - 4x) = -13
-x + 120 + 20x = -13
19x + 120 = -13
19x = -133
x = -7

Now that we have found the value of x, we can substitute it back into the first equation to find y:

4(-7) + y = -24
-28 + y = -24
y = -24 + 28
y = 4

Therefore, the solution to the system of equations is x = -7 and y = 4.