Solve for $x$. \[ \log _{5}(-2 x+5)=2 \] \[ x= \] \[ \frac{\square}{\square} \] $x$ 5

Step 1 ：To solve for $x$ in the equation $\log _{5}(-2 x+5)=2$, we can use the property of logarithms that says $a = b^c$ is equivalent to $\log_b(a) = c$. So, we can rewrite the equation as $-2x + 5 = 5^2$.

Step 2 ：Then, we can solve for $x$ by subtracting 5 from both sides of the equation and then dividing by -2.

Step 3 ：The solution to the equation is $x = -10$.

Step 4 ：Final Answer: $x = \boxed{-10}$