As your answer is given, it's impossible to solve because the result of the absolute value is always positive(or zero).
But if |5x+13|=7
The are 2 cases:
1. 5x+13=-7
5x=-20
x=-4
2. -(5x+13)=-7
5x+13=7
5x=-6
x=-6/5
I hope that this is the answer that you were looking for and it has helped you.