I want to begin this answer by saying that you should be careful using a phrase such as the "five pillars of management" just because if you do extensive research on the subject you will come up with multiple lists of different qualities. Unfortunately, you don't mention the source of your list, so it was impossible to give you quotations from the author who originally created your list. Your question was included under "reference" and has been changed to "business," because of the more specific content involved. Further, one of the newest books called The Five Pillars of TQM (Total Quality Management) has a very different list of qualities. That being said, it is pertinent that you included a detailed list because it enabled our eNotes Educators to give you a better answer. What follows is a good analysis of the five qualities you mention:
Leadership is the activity of managing a group of employees in order to allow them to collectively achieve a business goal. A leader will inspire employees under him or her and not just force them to perform. In order to make this happen, a leader needs to create a very clear vision, to make his or her clear vision known, to provide ways to make that vision happen (via both information and processes), and to coordinate conflict resolution regarding that clear vision. No doubt, there will be bumps in the road and a good leader will be able to manage those with creativity. Further, leadership is something innate and is impossible to be taught to another, it can only be augmented.
Communication is a process between a leader and a subordinate (or subordinates) where the two (or more) can reach a shared understanding. There is an exchange of ideas and information (even feelings sometimes). Put simply, it is a connection process meant to augment leadership and make that leadership more successful. It is impossible for a business to be successful without communication between owners, managers, leaders, employees, etc.
Negotiation is a specific type of communication (as indicated in the definition above). It is another process in business, but this time the process is between two (often opposing) people/groups who are working to achieve common ground, often among significant differences. It can be done between two opposing employees over the tutelage of a manager or even be done between two opposing businesses. Negotiation definitions can be tweaked to the specific business to provide even more specifics on the process.
Motivation is the process of inspiring employees to be successful (often as a collective group) in order to make a business thrive. Often there is a reward (or incentive) involved to achieve a common business goal. Monetary bonuses are a common motivation. Some motivation will be conscious and some will be unconscious. In some people, that motivation seems to be innate while in others it needs to be learned.