What is the solution set of 2x - 3 = 5 and 5x + 3 > -12?

To find the solution set for the equations and inequality given, we can solve them step by step.

1. **Solve the equation**:
\[
2x - 3 = 5
\]
Add 3 to both sides:
\[
2x = 8
\]
Now, divide by 2:
\[
x = 4
\]

2. **Solve the inequality**:
\[
5x + 3 > -12
\]
Subtract 3 from both sides:
\[
5x > -15
\]
Now, divide by 5:
\[
x > -3
\]

Now we combine the results:

- From the equation, we found \( x = 4 \).
- From the inequality, we found \( x > -3 \).

The solution set must satisfy both conditions. Since \( x = 4 \) is greater than \(-3\), it satisfies the inequality.

**Final Solution Set**:
The solution set is \(\{4\}\) because it is the value of \( x \) which satisfies both the equation and the inequality.