Let's simplify the given expression step by step.

The expression you provided is:

\[
(3x - 4)^2 + 2(3x - 4)(5 - x) + (x - 5)^2(3x - 4)^2 + 2(3x - 4)(5 - x) + (x - 5)^2
\]

First, we can notice that the expression consists of similar terms, particularly involving \( (3x - 4) \) and \( (5 - x) \).

We will first simplify the expression by combining similar terms where possible.

**Step 1: Simplify the first part**

The first part is:

\[
(3x - 4)^2 + 2(3x - 4)(5 - x) + (5 - x)^2
\]

This fits the form of the expansion of \( (A + B)^2 = A^2 + 2AB + B^2 \), where:

- \( A = (3x - 4) \)
- \( B = (5 - x) \)

Thus,

\[
(3x - 4 + (5 - x))^2 = (3x - x + 5 - 4)^2 = (2x + 1)^2
\]

So,

\[
(3x - 4)^2 + 2(3x - 4)(5 - x) + (5 - x)^2 = (2x + 1)^2
\]

**Step 2: Simplify the second part**

Now let's handle the remaining terms:

\[
(x - 5)^2(3x - 4)^2 + 2(3x - 4)(5 - x) + (x - 5)^2
\]

We notice that \( (x - 5)^2 = (5 - x)^2 \).

The second part can also contain \( 2(3x - 4)(5 - x) \) as is, so we can group terms again.

Thus we can rewrite it as:

\[
(3x - 4)^2(5 - x)^2 + 2(3x - 4)(5 - x) + (5 - x)^2
\]

Similar to the previous step, this can be expressed as:

\[
((3x - 4)(5 - x) + (5 - x))^2
\]

Since \( (5 - x) \) becomes a common term for both, this whole expression simplifies together.

**Combining Everything:**

Now, we can conclude the whole expression combines to produce:

\[
(2x + 1)^2 + (x - 5)^2(3x - 4)^2 + 2(3x - 4)(5 - x)
\]

Calculating this and simplifying, you will have your final answer.

In summary, the entire original expression simplifies to:

\[
(2x + 1)^2 + (5 x - 35)^2 (3x - 4)^2
\]

If you need the explicit expanded form of each, please provide specifics.