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 can solve each equation and see if 5 is the only solution.

1. **Equation 1: \( 2(x-3) + 1 = 5 \)**
Begin by simplifying the equation:

\[
2(x - 3) + 1 = 5
\]
\[
2(x - 3) = 4
\]
\[
x - 3 = 2
\]
\[
x = 5
\]

**Solution:** \( x = 5 \).

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

\[
b^{15} = \frac{1}{3}
\]

Taking the 15th root:

\[
b = \left(\frac{1}{3}\right)^{\frac{1}{15}}
\]

The value of \( b \) is approximately \( \frac{1}{3^{1/15}} \), which is not equal to 5.

**Solution:** No solution of \( b = 5 \).

3. **Equation 3: \( 2h - 30 = 40 \)**
Begin by simplifying the equation:

\[
2h - 30 = 40
\]
\[
2h = 70
\]
\[
h = 35
\]

**Solution:** \( h = 35 \) which is not equal to 5.

Now we can summarize the results:
- The first equation has a solution of \( x = 5 \).
- The second equation does not provide a solution of 5.
- The third equation's solution is \( h = 35 \), which is not 5.

Thus, the only equation that has the solution set {5} is the first one.

**The total number of equations that have the solution set {5} is:**

\(\text{1}\)