The domain of a log function is all values greater than zero. The log of a negative number is not real.
In this case, that means 
or 
(x-5)(x+1) < 0
x = 5 and x = -1
Because it's an inequality, set up intervals based on these roots, and test the equation in these intervals.
-infinity to -1, -1 to 5, and 5 to infinity. Since the inequality is greater than or =, the solution range will include the roots. You can plug them into the equation to prove it.
-infinity to -1: Use -10. -10^2 -4(-10) -5 = 135 > 0, so this interval is not part of the solution.
-1 to 5: Use 0. 0 - 0 -5 = -5 < 0, so this interval is part of the solution.
5 to infinity: Use 10. 10^2 - 4(10) - 5 = 55 > 0, so this interval is not part of the solution.
The domain is -1 <= x <= 5
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