Answer
$α \approx 67^{\circ}$
$β \approx 23^{\circ}$
Work Step by Step
1. Find $α$
$cos = \frac{adjacent}{hypotenuse}$
$cos(α) = \frac{5}{13}$
by GDC / calculator
$α = 67.380135...^{\circ}$
$α \approx 67^{\circ}$
2. Find $β$
$sin = \frac{opposite}{hypotenuse}$
$sin(β) = \frac{5}{13}$
by GDC / calculator
$β = 22.61986...^{\circ}$
$β \approx 23^{\circ}$