The main topic of this paper is the investigation of 5-pentagons whose interior angles are all right angles within the hyperbolic geometry (so-called 5-rectangles). Some knowledge of elementary hyperbolic geometry is required. At first the existence of such a polygon is shown by construction within the Kleinmodel. Then two formulas due to D. M. Y. Sommerville [3] are proved. This means to juggle with trigonometric formulas of hyperbolic geometry. In the last years a big number of papers concerning hyperbolic geometry was published. This proves that the interest in this nice discipline is growing again.