1. **Stating the problem:** We have a pentagon with side lengths: two diagonal sides of 5 units each, two vertical sides of 4 units each, and a base of 8 units. 2. **Goal:** Calculate the perimeter of the pentagon. 3. **Formula:** The perimeter $P$ of a polygon is the sum of the lengths of all its sides: $$P = \text{side}_1 + \text{side}_2 + \text{side}_3 + \text{side}_4 + \text{side}_5$$ 4. **Substitute the given side lengths:** $$P = 5 + 4 + 8 + 4 + 5$$ 5. **Calculate the sum:** $$P = (5 + 5) + (4 + 4) + 8 = 10 + 8 + 8$$ $$P = 26$$ 6. **Answer:** The perimeter of the pentagon is $26$ units.