To solve the inequalities:

1) 5x - 15 > 0
Add 15 to both sides:
5x > 15
Divide by 5:
x > 3

2) 6(x+1) > 5x + 3
Expand the left side:
6x + 6 > 5x + 3
Subtract 5x from both sides:
x + 6 > 3
Subtract 6 from both sides:
x > -3

So the solution to the inequalities is x > 3 and x > -3. However, the second inequality x > -3 is not necessary as it is already included in x > 3. So the final solution is x > 3.