Answer
The given logarithm is undefined.
Work Step by Step
Let
$x=\log_5{-25}.$
RECALL:
$\log_{a}{y} = b \longleftrightarrow a^b = y.$
Use the definition above to convert the equation to an exponential equation and have
$5^x=-25.$
Note $5$ is raised to any power, the result will never be negative.
Thus, the given equation has no solution.
This means that the given logarithmic expression is undefined.
