The problem is to solve the equation $9^{z+5}=3^z$ for the variable $z$.

1. Problem Description

The problem is to solve the equation $9^{z+5}=3^z$ for the variable $z$.

2. Solution Steps

First, we can rewrite the base 9 as $3^2$, so the left side of the equation becomes $(3^2)^{z+5}$.

$$(3^2)^{z+5} = 3^z$$

Using the power of a power rule, we get:

$$3^{2(z+5)} = 3^z$$

Since the bases are equal, the exponents must be equal. Therefore, we have:

$$2(z+5) = z$$

Distribute the 2 on the left side:

$$2z + 10 = z$$

Subtract $2z$ from both sides:

$$10 = z - 2z$$

$$10 = -z$$

Multiply both sides by -1 to solve for $z$:

$$z = -10$$

3. Final Answer

$z = -10$