Let's solve each equation step by step.

### Equation 1: \( 6(x - 2) - 1 = 3 \)

1. Distribute the 6:
\[
6(x - 2) = 6x - 12
\]
So the equation becomes:
\[
6x - 12 - 1 = 3
\]

2. Combine like terms:
\[
6x - 13 = 3
\]

3. Add 13 to both sides to isolate the term with \( x \):
\[
6x - 13 + 13 = 3 + 13
\]
\[
6x = 16
\]

4. Divide both sides by 6 to solve for \( x \):
\[
x = \frac{16}{6}
\]
Simplify the fraction:
\[
x = \frac{8}{3}
\]

So, the solution to the first equation is:
\[
x = \frac{8}{3}
\]

### Equation 2: \( (2x - 1)(x - 5) = 0 \)

This is a factored quadratic equation. For the product to be zero, at least one of the factors must be zero.

1. Set each factor equal to zero and solve for \( x \):

\[
2x - 1 = 0
\]
Add 1 to both sides:
\[
2x = 1
\]
Divide by 2:
\[
x = \frac{1}{2}
\]

\[
x - 5 = 0
\]
Add 5 to both sides:
\[
x = 5
\]

So, the solutions to the second equation are:
\[
x = \frac{1}{2} \quad \text{or} \quad x = 5
\]

### Summary of Solutions:
1. For \( 6(x - 2) - 1 = 3 \):
\[
x = \frac{8}{3}
\]

2. For \( (2x - 1)(x - 5) = 0 \):
\[
x = \frac{1}{2} \quad \text{or} \quad x = 5
\]