To solve the equation \(5(x + 7) + 3(x - 5) = 36\), follow these steps:

1. Distribute the constants inside the parentheses:
\[
5(x + 7) + 3(x - 5) = 36
\]
\[
5x + 35 + 3x - 15 = 36
\]

2. Combine like terms:
\[
5x + 3x + 35 - 15 = 36
\]
\[
8x + 20 = 36
\]

3. Isolate the variable term by subtracting 20 from both sides:
\[
8x + 20 - 20 = 36 - 20
\]
\[
8x = 16
\]

4. Solve for \(x\) by dividing both sides by 8:
\[
x = \frac{16}{8}
\]
\[
x = 2
\]

So, the solution to the equation \(5(x + 7) + 3(x - 5) = 36\) is \(x = 2\).