This is an isosceles triangle. Therefore, at the base we have congruent angles (look at the picture).
We have the equation:
(5x + 13)° + (3x + 7)° = 180°
5x + 13 + 3x + 7 = 180 combine like terms
(5x + 3x) + (13 + 7) = 180
8x + 20 = 180 subtract 20 from both sides
8x = 160 divide both sides by 8
x = 20