To simplify the provided algebraic expressions, let's work through each one step by step.

### 5. \((x+2)(x-3)+x(x+1)\)

1. Expand:
\[
(x^2 - 3x + 2x - 6) + (x^2 + x) = x^2 - x - 6 + x^2 + x
\]
2. Combine like terms:
\[
2x^2 - 6
\]

### 6. \((2x-1)(x+1)+x(2x-5)\)

1. Expand:
\[
(2x^2 + 2x - x - 1) + (2x^2 - 5x) = 2x^2 + x - 1 + 2x^2 - 5x
\]
2. Combine like terms:
\[
4x^2 - 4x - 1
\]

### 7. \(x(1-x)+(x+1)(x-2)\)

1. Expand:
\[
(x - x^2) + (x^2 - 2x + x - 2) = -x^2 + 3x - 2
\]
2. Rearrange:
\[
-x^2 + 3x - 2
\]

### 8. \((3x-1)(x+4)-3x(x-1)\)

1. Expand:
\[
(3x^2 + 12x - x - 4) - (3x^2 - 3x) = 3x^2 + 11x - 4 - 3x^2 + 3x
\]
2. Combine like terms:
\[
14x - 4
\]

### 9. \(2x(x-3)+(x-2)(5-2x)\)

1. Expand:
\[
(2x^2 - 6x) + (5x - 10 - 2x^2 + 4x) = 2x^2 - 6x + 5x - 10 - 2x^2 + 4x
\]
2. Combine like terms:
\[
3x - 10
\]

### 10. \(6x(2x+3)-(3x-1)(4x+1)\)

1. Expand:
\[
12x^2 + 18x - (12x^2 + 3x - 4x - 1) = 12x^2 + 18x - 12x^2 - 3x + 4x + 1
\]
2. Combine like terms:
\[
19x + 1
\]

### 11. \(3x(4x-3)-(2x-1)(6x+5)\)

1. Expand:
\[
(12x^2 - 9x) - (12x^2 + 10x - 6x - 5) = 12x^2 - 9x - 12x^2 - 10x + 6x + 5
\]
2. Combine like terms:
\[
-13x + 5
\]

### 12. \((2-5x)(3-4x)+x(2x+23)\)

1. Expand:
\[
(6 - 8x - 15x + 20x^2) + (2x^2 + 23x) = 20x^2 - 23x + 6 + 2x^2 + 23x
\]
2. Combine like terms:
\[
22x^2 + 6
\]

### 13. \(3(x-1)(x-2)-x(3x+1)(1-x)\)

1. Expand:
\[
3(x^2 - 3x + 2) - x(3x + 1 - 3x^2 - x) = 3x^2 - 9x + 6 - x(-2x + 1)
\]
2. Combine like terms:
\[
-x^2 - 8x + 6
\]

### 14. \(-4x(x+3)(x-4)-3x(x^2-x+1)\)

1. Expand:
\[
-4x(x^2 - x - 12) - 3x(x^2 - x + 1) = -4x^3 + 4x^2 + 48x - 3x^3 + 3x^2 - 3x
\]
2. Combine like terms:
\[
-7x^3 + 7x^2 + 45x
\]

### 15. \(-3(x+4)(x-7)+7(x-5)(x-1)\)

1. Expand:
\[
-3(x^2 - 3x - 28) + 7(x^2 - 6x + 5)= -3x^2 + 9x + 84 + 7x^2 - 42x + 35
\]
2. Combine like terms:
\[
4x^2 - 33x + 119
\]

### 16. \(-2(x-3)(2x^2+1)+x(4x+1)(x+2)\)

1. Expand:
\[
-2(2x^3 - 6x^2 + 1 - 2) + x(4x^2 + 8x + x + 2) = -4x^3 + 12x^2 - 2 + 4x^3 + 9x + 2
\]
2. Combine like terms:
\[
12x^2 + 9x
\]

By simplifying all expressions, you get the final simplified forms:

1. \(2x^2 - 6\)
2. \(4x^2 - 4x - 1\)
3. \(-x^2 + 3x - 2\)
4. \(14x - 4\)
5. \(3x - 10\)
6. \(19x + 1\)
7. \(-13x + 5\)
8. \(22x^2 + 6\)
9. \(-x^2 - 8x + 6\)
10. \(-7x^3 + 7x^2 + 45x\)
11. \(4x^2 - 33x + 119\)
12. \(12x^2 + 9x\)