Let's solve each of these equations step by step:

1. \( (2x-1)^2 - (4x^2-1) = 0 \)

First, expand both squares:

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

Substitute these into the equation:

\[
4x^2 - 4x + 1 - (4x^2 - 1) = 0
\]

Simplify:

\[
4x^2 - 4x + 1 - 4x^2 + 1 = 0
\]

The \(4x^2\) terms cancel each other out:

\[
-4x + 2 = 0
\]

Solve for \(x\):

\[
-4x = -2
\]
\[
x = \frac{1}{2}
\]

2. \( (x+2)^2 - x(x-3) = 2 \)

Expand the terms:

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

Substitute these into the equation:

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

Simplify:

\[
x^2 + 4x + 4 - x^2 + 3x = 2
\]

Combine like terms:

\[
7x + 4 = 2
\]

Solve for \(x\):

\[
7x = -2
\]
\[
x = -\frac{2}{7}
\]

3. \( (x-5)^2 - x(x+2) = 5 \)

Expand the terms:

\[
(x-5)^2 = x^2 - 10x + 25
\]
\[
x(x+2) = x^2 + 2x
\]

Substitute these into the equation:

\[
x^2 - 10x + 25 - (x^2 + 2x) = 5
\]

Simplify:

\[
x^2 - 10x + 25 - x^2 - 2x = 5
\]

Combine like terms:

\[
-12x + 25 = 5
\]

Solve for \(x\):

\[
-12x = -20
\]
\[
x = \frac{5}{3}
\]

4. \( (x-1)^2 + x(4-x) = 11 \)

Expand the terms:

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

Substitute these into the equation:

\[
x^2 - 2x + 1 + 4x - x^2 = 11
\]

Simplify:

\[
x^2 - 2x + 1 + 4x - x^2 = 11
\]

Combine like terms:

\[
2x + 1 = 11
\]

Solve for \(x\):

\[
2x = 10
\]
\[
x = 5
\]

5. \( (x-3)(x+3) = (x-5)^2 \)

Expand the terms:

\[
(x-3)(x+3) = x^2 - 9
\]
\[
(x-5)^2 = x^2 - 10x + 25
\]

Substitute these into the equation:

\[
x^2 - 9 = x^2 - 10x + 25
\]

Simplify and solve for \(x\):

\[
-9 = -10x + 25
\]

Rearrange:

\[
-10x = -34
\]
\[
x = \frac{34}{10} = \frac{17}{5}
\]

These are solutions for each equation.