Let's calculate the values of \(A\), \(B\), \(C\), and \(D\) step by step.

### 1. Calculating \(A\) at \(x = 3\):

\[
A = (x - 2)(x^4 + 2x^3 + 4x^2 + 8x + 16)
\]

Substituting \(x = 3\):

\[
A = (3 - 2) (3^4 + 2 \cdot 3^3 + 4 \cdot 3^2 + 8 \cdot 3 + 16)
\]

Calculating each term:
- \(3^4 = 81\)
- \(2 \cdot 3^3 = 2 \cdot 27 = 54\)
- \(4 \cdot 3^2 = 4 \cdot 9 = 36\)
- \(8 \cdot 3 = 24\)
- \(16 = 16\)

Now, summing these values:

\[
81 + 54 + 36 + 24 + 16 = 211
\]

Finally, substituting back into \(A\):

\[
A = 1 \cdot 211 = 211
\]

### 2. Calculating \(B\) at \(x = 2\):

\[
B = (x + 1)(x^7 - x^6 + x^5 - x^4 + x^3 - x^2 + x - 1)
\]

Substituting \(x = 2\):

\[
B = (2 + 1)(2^7 - 2^6 + 2^5 - 2^4 + 2^3 - 2^2 + 2 - 1)
\]

Calculating each power of 2:
- \(2^7 = 128\)
- \(2^6 = 64\)
- \(2^5 = 32\)
- \(2^4 = 16\)
- \(2^3 = 8\)
- \(2^2 = 4\)

Now substituting and simplifying:

\[
B = 3(128 - 64 + 32 - 16 + 8 - 4 + 2 - 1)
\]
\[
= 3(85)
\]
\[
= 255
\]

### 3. Calculating \(C\) at \(x = 2\):

\[
C = (x + 1)(x^6 - x^5 + x^4 - x^3 + x^2 - x + 1)
\]

Substituting \(x = 2\):

\[
C = (2 + 1)(2^6 - 2^5 + 2^4 - 2^3 + 2^2 - 2 + 1)
\]

Calculating each power of 2 as before:

\[
C = 3(64 - 32 + 16 - 8 + 4 - 2 + 1)
\]
\[
= 3(43)
\]
\[
= 129
\]

### 4. Calculating \(D\) at \(x = -5\):

\[
D = 2x(10x^2 - 5x - 2) - 5x(4x^2 - 2x - 1)
\]

Substituting \(x = -5\):

\[
D = 2(-5)(10(-5)^2 - 5(-5) - 2) - 5(-5)(4(-5)^2 - 2(-5) - 1)
\]

Calculating the quadratic expressions:

For the first term:
\[
10(-5)^2 = 10 \cdot 25 = 250,\quad -5(-5) = 25,\quad -2 = -2
\]
So,
\[
= 10(-5)(250 + 25 - 2) = 10(-5)(273) = -1365
\]

For the second term:
\[
4(-5)^2 = 4 \cdot 25 = 100,\quad -2(-5) = 10,\quad -1 = -1
\]
So,
\[
= -5(-5)(100 + 10 - 1) = 25(109) = 2725
\]

Combining both contributions to \(D\):

\[
D = -1365 + 2725 = 1360
\]

### Summary of Results:
- \(A = 211\)
- \(B = 255\)
- \(C = 129\)
- \(D = 1360\)