All the 32 subsets for (x,y,z,u,v)

Answer 1

No shortcuts here. Just start listing them, in order of number of elements:

{}
{x},{y},...
{x,y},{x,z},...
{x,y,z},{x,y,u},...
{x,y,z,u},{x,y,z,v},...
{x,y,z,u,v}