The aspiration to replicate the capabilities of the human hand has driven innovations in the design of soft robotic hands. Despite these advancements, many existing designs of soft hands still lack effective in-hand vision and the ability for each finger to achieve active multi-degree-of-freedom motion. This paper proposes a cable-driven soft robotic hand that can achieve dexterous grasping and manipulation, vision-guided grasping, vision-based slip detection and compensation, as well as visually servoed in-hand manipulation. The hand has five soft fingers, each capable of independent flexion/extension motion and bidirectional ad/abduction motion. A red-green-blue-depth (RGB-D) camera is integrated into the palm of the soft hand to enable in-hand vision capability. Modeling of the soft hand is established to analyze its kinematics, statics, and manipulability. A series of experiments are conducted to demonstrate its dexterous grasping and manipulation capabilities on a variety of objects. Using 3D point cloud data from the in-palm camera, an effective vision-guided grasping strategy is developed to grasp objects on a table. The in-hand vision also enables slip detection and compensation during grasping to maintain the grasp stability. Furthermore, a hierarchical, visually servoed controller is developed to perform closed-loop in-hand object manipulation. With its high dexterity and visual feedback capabilities, the soft hand will find important applications such as household object manipulation and food picking/sorting, and may also be used as a prosthetic hand or an auxiliary hand for humans.