We get Z-fighting when we extrude the pentagon(already having a face) at 3.58.. why Don't we get some similar issue if we are doing a similar thing at 4.42? What's the difference?
The difference is that a face is selected at 3:58 but not at 4:42.
At 3:58, we have selected all 5 vertices that are connected to make a face, so by relation we have also selected the face. When extruding from a face, Blender assumes that you're going to be extruding upwards (like you're turning a circle into a cylinder), so it gives the face that you're extruding from sides and end caps. When these elements are scaled outwards, the original face, the sides, and the end caps all lay on top of each other causing the z-fighting artifact.
At 4:42 we do not have a face selected. Instead, we have 5 vertices. When you extrude from vertices, Blender only adds sides, so there is no end cap laying on top of things causing z-fighting.
Below is an image demonstrating two of these. On the left, we have a plane that has a layer added outside of the main face, so when we extrude we're only extruding from vertices. On the right, the plane did not have that extra layer, so when we selected the four corner vertices (and inherently, the face) Blender assumed that we wanted to extrude into a cube and added that extra end cap to top things off.
