To determine how many of the given equations have the solution set \({5}\), we will solve each equation one by one.
First equation: \[ 2(x - 3) + 1 = 5 \] Start by simplifying: \[ 2(x - 3) + 1 = 5 \implies 2(x - 3) = 5 - 1 \implies 2(x - 3) = 4 \] Now divide by 2: \[ x - 3 = 2 \implies x = 5 \] This equation has the solution \(x = 5\).
Second equation: \[ \frac{3b}{15} = 1 \] Simplify the left side: \[ \frac{b}{5} = 1 \] Now multiply both sides by 5: \[ b = 5 \] This equation has the solution \(b = 5\).
Third equation: \[ 2h - 30 = 40 \] Add 30 to both sides: \[ 2h = 70 \] Now divide by 2: \[ h = 35 \] This equation has the solution \(h = 35\), which does not equal 5.
Now, we summarize the findings:
- The first equation has the solution \(x = 5\).
- The second equation has the solution \(b = 5\).
- The third equation does not have the solution \(h = 5\).
Thus, the total number of equations that have the solution set \({5}\) is:
\[ \boxed{2} \]