Apply the logarithm property a + b = (ab).

The given equation is:

$$\ln(x+3) + \ln(x+5) = \ln15$$

Using the property, we combine the terms on the left side:

$$\ln((x+3)(x+5)) = \ln15$$

Since the natural logarithm is a one-to-one function, if $\ln A = \ln B$, then $A=B$.

$$(x+3)(x+5) = 15$$

Expand the left side:

$$x^2 + 5x + 3x + 15 = 15$$ $$x^2 + 8x + 15 = 15$$

Subtract 15 from both sides:

$$x^2 + 8x = 0$$

Factor out $x$:

$$x(x+8) = 0$$

This gives two potential solutions:

$$x = 0 \quad \text{or} \quad x+8 = 0 \implies x = -8$$

For $\ln(x+3)$ to be defined, $x+3 > 0 \implies x > -3$.
For $\ln(x+5)$ to be defined, $x+5 > 0 \implies x > -5$.
Both conditions must be satisfied, so we need $x > -3$.

Let's check our potential solutions:

• For $x=0$: $0 > -3$. This condition is satisfied. Substituting $x=0$ into the original equation: $\ln(0+3) + \ln(0+5) = \ln3 + \ln5 = \ln(3 \times 5) = \ln15$. This is correct. So, $x=0$ is a valid solution.

• For $x=-8$: $-8 > -3$. This condition is NOT satisfied. Substituting $x=-8$ into the original equation would give $\ln(-8+3) = \ln(-5)$ and $\ln(-8+5) = \ln(-3)$, which are undefined in the set of real numbers. So, $x=-8$ is not a valid solution.

Therefore, the only valid solution is $x=0$.

Based on our analysis, the correct option is A.

The final answer is $\boxed{\text{A) x=0 only}}$.