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

To determine how many of the equations have the solution set \({5}\), we will solve each equation separately and check if \(x = 5\), \(b = 5\), and \(h = 5\) satisfy them.

1. **Equation 1:**
\[
2(x - 3) + 1 = 5
\]
Simplifying the left side:
\[
2x - 6 + 1 = 5
\]
\[
2x - 5 = 5
\]
\[
2x = 10
\]
\[
x = 5
\]
\(x = 5\) is a solution.

2. **Equation 2:**
\[
3b^{15} = 1
\]
To isolate \(b\), divide both sides by 3:
\[
b^{15} = \frac{1}{3}
\]
To solve for \(b\):
\[
b = \left(\frac{1}{3}\right)^{\frac{1}{15}}
\]
This value is not equal to 5, so \(b = 5\) is not a solution.

3. **Equation 3:**
\[
2h - 30 = 40
\]
Adding 30 to both sides:
\[
2h = 70
\]
Dividing by 2:
\[
h = 35
\]
This value is not equal to 5, so \(h = 5\) is not a solution.

Now, summarizing the results:
- Equation 1 has the solution \(x = 5\).
- Equation 2 does not have the solution \(b = 5\).
- Equation 3 does not have the solution \(h = 5\).

Only the first equation has the solution \(5\).

Therefore, the number of equations that have the solution set \(\{5\}\) is **1**.