How many of the following equations have the solution set {5}

To determine how many of the provided equations have the solution set {5}, we need to solve each equation for the variable and see if it equals 5.

1. **Equation 1:** \( 2(x-3) + 1 = 5 \)

\[
2(x-3) + 1 = 5
\]
Subtract 1 from both sides:
\[
2(x-3) = 4
\]
Divide both sides by 2:
\[
x-3 = 2
\]
Add 3 to both sides:
\[
x = 5
\]

**This equation has the solution 5.**

2. **Equation 2:** \( 3b = 15 \)

To isolate \( b \):
\[
b = \frac{15}{3} = 5
\]

**This equation has the solution 5.**

3. **Equation 3:** \( 2h - 30 = 40 \)

Add 30 to both sides:
\[
2h = 70
\]
Divide by 2:
\[
h = 35
\]

**This equation does not have the solution 5.**

Now, let's summarize the results:
- First equation has the solution 5.
- Second equation has the solution 5.
- Third equation does not have the solution 5.

Thus, the total number of equations that have the solution {5} is **2**.

So, the answer is:
The number of equations that have the solution set {5} is **2**.