This study presents the compact zoom lens with a zoom ratio of 5x for a mobile camera by using a prism. The lens modules and aberrations are applied to the initial design for a four-group inner-focus zoom system. An initial design with a focal length range of 4.4 to 22.0 mm is derived by assigning the first-order quantities and third-order aberrations to each module along with the constraints required for optimum solutions. We separately designed a real lens for each group and then combined them to establish an actual zoom system. The combination of the separately designed groups results in a system that satisfies the basic properties of the zoom system consisting of the original lens modules. In order to have a slim system, we directly inserted the right-angle prism in front of the first group. This configuration resulted in a more compact zoom system with a depth of 8 mm. The finally designed zoom lens has an f-number of 3.5 to 4.5 and is expected to fulfill the requirements for a slim mobile zoom camera having high zoom ratio of 5x.