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 need to check if each equation is satisfied when \( x = 5 \).

1. **Equation**: \( 2(x−3)+1=5 \)

Substitute \( x = 5 \):
\[
2(5−3)+1 = 2(2)+1 = 4+1 = 5
\]
This equation is satisfied.

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

To solve for \( b \):
\[
b^{15} = \frac{1}{3}
\]
\( b = \left(\frac{1}{3}\right)^{\frac{1}{15}} \). This does not equal 5, so this equation is not satisfied.

3. **Equation**: \( 2h−30=40 \)

Substitute \( h = 5 \):
\[
2(5)−30 = 10−30 = -20 \neq 40
\]
This equation is also not satisfied.

Now, let's summarize the results:

- The first equation is satisfied when \( x = 5 \).
- The second equation is not satisfied when \( b = 5 \).
- The third equation is not satisfied when \( h = 5 \).

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

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