Solve for $x$ \[ 25^{x+4}=125 \] \[ x= \]

Step 1 ：The given equation is \(25^{x+4}=125\).

Step 2 ：We can rewrite 25 as \(5^2\) and 125 as \(5^3\). So, the equation becomes \((5^2)^{x+4}=5^3\).

Step 3 ：Simplifying the equation, we get \(5^{2x+8}=5^3\).

Step 4 ：Since the bases are the same, the exponents must be equal. So, we have \(2x+8=3\).

Step 5 ：Solving this equation for x, we get \(x=-\frac{5}{2}\).

Step 6 ：So, the solution to the equation \(25^{x+4}=125\) is \(x=-\frac{5}{2}\).

Step 7 ：Final Answer: \(x=\boxed{-\frac{5}{2}}\)