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

To determine how many of the given equations have the solution set {5}, we will solve each equation for the variable.

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

Solve for \(x\):
\[
2(x - 3) + 1 = 5
\]
\[
2(x - 3) = 4 \quad \text{(subtracting 1 from both sides)}
\]
\[
x - 3 = 2 \quad \text{(dividing both sides by 2)}
\]
\[
x = 5 \quad \text{(adding 3 to both sides)}
\]

This equation has the solution \(x = 5\).

2. **Equation: \(3b^{15} = 1\)**

Solve for \(b\):
\[
b^{15} = \frac{1}{3} \quad \text{(dividing both sides by 3)}
\]
To find \(b\):
\[
b = \left( \frac{1}{3} \right)^{\frac{1}{15}}
\]

The value of \(b\) is not \(5\). So this equation does not have the solution \(b = 5\).

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

Solve for \(h\):
\[
2h = 70 \quad \text{(adding 30 to both sides)}
\]
\[
h = 35 \quad \text{(dividing both sides by 2)}
\]

This equation does not have the solution \(h = 5\).

Now, let's summarize the results:
- The first equation has the solution \(x = 5\).
- The second equation has the solution \(b \approx 0.464\) (which is not 5).
- The third equation has the solution \(h = 35\) (which is not 5).

Thus, only **1 equation** has the solution set \{5\}.

The number of equations that have the solution set \{5\} is **1**.