1. **Problem Statement:** Find the volume of the solid composed of five 1-centimeter cubes arranged with four cubes in a 2 by 2 base layer and one cube stacked on top of the back row left cube. 2. **Formula and Explanation:** Volume of a solid made of unit cubes is the total number of cubes since each cube has volume $1 \text{ cm}^3$. 3. **Step-by-step Solution:** 1. Count the cubes in the base layer: $2 \times 2 = 4$ cubes. 2. Count the cubes stacked on top: $1$ cube. 3. Total volume = base cubes + stacked cubes = $4 + 1 = 5$ cubic centimeters. 4. **Final Answer:** $$\text{Volume} = 5 \text{ cm}^3$$