Let's simplify the inequality step by step:

2x + 8 > -5(x - 3)
2x + 8 > -5x + 15 (distribute -5 on the right side)
2x + 8 + 5x > 15 (add 5x to both sides)
7x + 8 > 15 (combine like terms)

Now, subtract 8 from both sides:
7x > 7

Finally, divide by 7:
x > 1

So, the solution for the inequality 2x + 8 > -5(x - 3) is x > 1.