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The equation presented is:

\[
5^{\sqrt{x+5}} = 25^{x+5}
\]

To solve for \( x \), we can simplify the equation by expressing both sides with a common base.

### Step 1: Rewrite \( 25 \) as \( 5^2 \)

Since \( 25 = 5^2 \), we can rewrite the right side of the equation as:
\[
25^{x+5} = (5^2)^{x+5} = 5^{2(x+5)}
\]

### Step 2: Substitute and Simplify

The equation now becomes:
\[
5^{\sqrt{x+5}} = 5^{2(x+5)}
\]

Since the bases are the same, we can set the exponents equal to each other:
\[
\sqrt{x+5} = 2(x+5)
\]

### Step 3: Solve the Equation

1. Square both sides to eliminate the square root:
   \[
   x + 5 = 4(x + 5)^2
   \]


Explore how to solve the exponential equation 5^(sqrt(x+5)) = 25^(x+5) by rewriting 25 as 5^2 and equating exponents. This problem covers exponentiation, radicals, and algebraic principles suitable for students in Grades 10-12.

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