1. Problem statement: Verify whether $\log_5 25 = 2$. 2. Formula and important rules: By definition, $\log_b a = c \iff b^c = a$. Important rules: The base $b$ must be positive and $b \ne 1$, and the argument $a$ must be positive. 3. Intermediate work: Rewrite 25 as a power of 5, since $25 = 5^2$. 4. Evaluation: Because $5^2 = 25$, by the definition of logarithm we have $\log_5 25 = 2$. 5. Final answer: The statement $\log_5 25 = 2$ is correct and the value is $2$.