Let’s first understand where from the number 5 will come? The stress applied on the body resolved into 9 components. Like sigma xx,yy,zz and tou xy,xz,yz… . Similarly we can write for strain also. We know that stress and strain matrix both are symmetric matrix. Because of the symmetry the 9 components reduces to 6 components. That is 3 normal stain components and 3 shear strain components. Now, we assumed that there is no change in volume during plastic deformation. That means strain xx + strain yy + strain zz = 0. From this relation this 6 components reduces to 5 components. Now, you may think how I am relating this stress and strain to slip system. For that we need to understand subscript of stress ( sigma xx or xy..). The first letter x represents plane where the stress acting and the second subscript x or y represents the direction the stress is acting. That means it simply represents plane and direction. The combination of both is we considered as slip system. That’s why we are relating stress tensor and slip systems.
What happen if there is no 5 slip systems?
During deformation of polycrystalline materials, It need to maintain continuity across the boundary. To maintain this continuity we required 5 independent slip system. If there is less than that 5 independent slip systems, It cannot maintain the continuity. So, it will form crack or void. That is reason, we need atleast 5 independent slip system for ductile behavior. In good ductile material the initiation of crack or void is difficult.