To simplify the expression \((x + 3)(x^2 + 3x - 5)(x + 3)(x^2 + 3x - 5)\), we can first observe that it contains a repeated factor. We can group the factors as follows:

\[
[(x + 3)(x^2 + 3x - 5)]^2.
\]

Next, we will simplify the expression inside the brackets, \( (x + 3)(x^2 + 3x - 5) \).

Using the distributive property (FOIL), we multiply the terms:

1. \( x \cdot x^2 = x^3 \)
2. \( x \cdot 3x = 3x^2 \)
3. \( x \cdot (-5) = -5x \)
4. \( 3 \cdot x^2 = 3x^2 \)
5. \( 3 \cdot 3x = 9x \)
6. \( 3 \cdot (-5) = -15 \)

Combining these results:

\[
x^3 + 3x^2 - 5x + 3x^2 + 9x - 15.
\]

Now we can combine like terms:

1. The \(x^2\) terms: \(3x^2 + 3x^2 = 6x^2\).
2. The \(x\) terms: \(-5x + 9x = 4x\).

Thus, we get:

\[
x^3 + 6x^2 + 4x - 15.
\]

Therefore, the expression can be rewritten as:

\[
\left(x^3 + 6x^2 + 4x - 15\right)^2.
\]

This is the simplified form of the original expression:

\[
(x + 3)(x^2 + 3x - 5)(x+3)(x^2+3x-5) = \left(x^3 + 6x^2 + 4x - 15\right)^2.
\]